An academic overanalysis for your reading pleasure:
Edit: "Dear Dave"
In Series 3, Episode 6 of Red Dwarf, "The Last Day", we learn that Dave Lister "didn't have a mum"; he was found in a box under a pool table in a pub. His adopted parents (his adopted father died when he was 6, and his mother remarried) and grandmother raised him, but it sounds like he didn't have a strong family upbringing, while still holding all of his father-figures in very high regard.
In "Ouroboros", we learn that, due to some timey-wimey travel, Lister is his own biological father, and Kristine Kochanski from a parallel universe is his mum (and girlfriend).
In the most recent entry into Red Dwarf lore, "Fathers and Suns", Dave explores parenthood/sonhood by having drunken fatherly conversations with himself. But this isn't the first time Dave has talked to himself.. older scenes are definitely seen in a different light when you see them in this context.
We can not forget that Lister discovers himself to be the "father" of an entire civilization, and the closest thing to a father figure that the Cat will ever have. But the two act more like mischievous brothers than "father and son". And knowing what we know now, if they do have a spiritual father-son relationship, they also have a spiritual brotherhood. In this sense, Lister is even more of a Jesus figure, both the Father and the Son, the Beginning and the End.. (it's also not lost that Kochanski's first name is Kristine, "Follower of Christ"), but I don't want to start any religious wars about colored hats here. Let's get back to the fun stuff!
The very first time Lister talks to himself is really early on: Series 1, Episode 2, "Future Echoes". "This is you, age 171, Dave." Old Lister, on his deathbed in his old bunk, complete with grey dreadlocks and mechanical bottle-opening hand, explains: "It wasn't you Rimmer saw in the drive room [when the computer exploded]; it was Bexley."
Old Lister never refers to Bexley as his son. It is "our" Lister, who hasn't yet found out about his parents, who immediately jumps to the conclusion that Bexley is his second son. Old Lister already knew that he was his own dad, and that he'd live on in the eternal cycle of life.. He also knew that Bexley was not only his son but his brother (although he was technically mother to the twins and father to himself). Not wanting to confuse the issue, or reveal too much about the future, he gave only the relevant details.
Lister runs down to the medical bay and witnesses the birth of his twins, his first children.
In Series 2, Episode 2, "Better than Life", Lister recounts the story of when his adopted father died. He really loved his dad, trying to send food down the toilet and read the football scores with his head in the bowl when he was told that dad went the same place as his goldfish. He really had a love for his father. And when his mother remarried, he established some kind of connection with her new husband, too. In "Marooned" (S3E2), the "final moments" with his guitar are to play a bittersweet song he learned from his stepdad.
Jump to Series 2, Episode 6, "Parallel Universe". This is the third time Dave Lister meets another one of himself, (and coincidentally a resolution to the Future Echoes plot). This is Deb Lister. Presumably, in her universe, she is also her own father -- her mom being Kristopher Kochanski from yet a fourth universe? -- and also doesn't know it yet.
Now wrap your head around this:
Dave and Deb Lister (effectively the same person) are their own fathers. Created out of themselves in a time-loop. They are also the mother and father of twin boys, Jim and Bexley. Jim and Bexley have two parents that never began existing and will never end existing. And Deb and Dave are also Jim and Bexley's younger half-siblings. No wonder they grew to 18 years old in 3 days ("Backwards")! These twins are the River Songs of the Red Dwarf Universe. Their DNA is Time and Existence itself.
Where are Jim and Bexley now? Perhaps they've disappeared in a horrible paradox accident. Perhaps they are the most powerful beings in two universes. This is also a good time to point out that Old Lister never said anything about Bexley dying in the Future Echo. He said it was Bexley that Rimmer saw in the Drive Room. If the twins are effectively gods, then this makes a big difference.
Now a step back for a moment, to S2E5, Stasis Leak. In this episode, the first one with actual time travel, we see a version of Lister from "5 years in the future", who has traveled back in time to marry Kochanski (the one from his universe). Arguably, this future doesn't exist anymore, because it didn't happen. But Future Lister does seem to treat Our Lister like a bratty son, doesn't he? And maybe Kochanski has a little bit of maternal instinct toward him? Perhaps her "Oh, it's you" comment means that this isn't the first time that Dad and Son have gotten together in the last 5 years.
As another aside: From the introduction of Kryten in Series 2, through at least Series 5, Lister is also something of a father figure to Kryten (much like with the Cat). Lister teaches Kryten all about lying, cheating, "being human"... it really shows that Lister *wants* to be a dad.
During the episode "Backwards" (S3E1), we see Lister's fear of degenerating into a fetus, and then a sperm, if he's left in the Backwards Earth for 25 years. Lucky that he didn't stay, because this "time lord" un-aging and being un-born and un-conceived would certainly spawn more paradoxes.
And this brings us to the most poignant Father/Son moment of all: "Timeslides" (S3E5).
Through a questionably-plausible time travel technique, Dave Lister (age "late 20s") sits down to chat with Dave Lister (age 17), lead singer of Smeg and the Heads. This is a true Father/Son conversation. Dad (ironically referred to by young Lister as "granddad", which he also technically is) is so "cryptofascist" and doesn't understand young people. "If you take your own chances, you'll wind up stuck on a spaceship with him, him, and him... for the rest of eternity. You won't _have_ a future," says our Lister, who is totally "sick of it". These are the final words from Dad to Son, and Son actually listens, despite his outward defiance (as teenage sons often do).
So 17-year-old Lister invents the Tension Sheet, becoming a super rockstar, the richest man who ever lived, dying happy at a ripe old age. At some point between 17 and 98, Lister (who never enrolled in the Space Corps) manages to acquire some time travel technology, woo Officer Kochanski (maybe on shore leave), and conceive himself, shedding the depressing-but-cosmically-important time loop, and instead creating a new time loop of existence where he is eternally happy. He has reached his reward in Heaven, so to speak.
Until, of course, Bonehead Rimmer and Thickie Holden rip Lister back out of his Heaven and into Reality, to serve out his true purpose of keeping the human race alive forever after their near-extinction.
In "DNA" (S4E2), Lister turns into a female chicken (the last chicken alive?) and almost lays an egg. Now that would lead to some interesting father/son conversations. Moving on...
"Dimension Jump" (S4E5) introduces us to the parallel universe that is the origin of Arnold "Ace" Rimmer -- and more importantly, David "Spanners" Lister. Spanners is happily married to Kochanski, with twin boys, Jim and Bexley. These twins are not the same Jim and Bexley that our Lister has fathered. In fact, Spanners probably knows his real parents, grew up with a stable home, isn't stuck in a time-loop, and just happens to be the cosmic equivalent of our Dave. This is one possible father Lister could have been, if circumstances were different.
Series 5 brings us more alternative versions of Lister ("Inquisitor", "Demons and Angels", even "Back to Reality"), but none of them address the father/son relationship, not even by my stretch of interpretation :)
OK, I take that back a little bit. In "Back to Reality" (S5E6), Lister's subconscious, brought on by the Despair Squid, and personified by Andy the attendant, hints that Lister knows he can not give up until he has found Kochanski. Not for True Love, but for keeping the Ouroboros cycle going.
In "Psirens" (S6E1), we see that Lister is still holding on to his dream, as a Psiren exploits his subconscious by appearing as Kochanski and mentioning their sons Jim and Bexley. Again, these aren't the same Jim and Bexley that Lister gave birth to. His subconscious mind just still has the imprint that his first 2 sons will have these names, and this is the strongest emotion that the Psirens can grab. (Once this fails, a Psiren tries a more vulnerable memory, Pete Tranter's sister, of course).
"Out of Time" (S6E6) shows us yet another potential future Lister, a selfish and "evil" future self, which inspires our Lister to fight. "What have I got to lose? Me jar?"
When "our" Lister dies, it is not Rimmer's sudden selfless burst of heroism that fixes the timelines. It is the temporal paradox itself. Without Lister alive, none of this could have ever happened. He must exist. He must find Kochanski. He must be born. Because it already "will-have-going-to-have-happened" happened.
After that point, we reach Series 7, which brings us back to the beginning again. The British version of "How I Met Your Mother", so to speak.
And then, skipping Series 8 and Back to Earth, which don't really address this part of the plot...
...we get to "Fathers and Suns" (SXE2). By this time, Lister knows the deal with his fate, and is taking it in stride. You can take or leave the rest of the episode, but the scenes of Lister and Lister show that he is a truly repentant father for all of the things he has done wrong, and understands the lessons he wished he had learned from his absent adopted father/stepfather; we only wish he has a chance to have the same conversations with Jim and Bexley someday.. Maybe they've talked to their dad (Deb) already, somewhere and sometime.
"Dear Dave" (SXE5) is another episode where Lister explores his thoughts on fatherhood. Once again forgetting about his other "children" -- even though he just addressed his own self-paternity 3 episodes ago -- he thinks about the fact that he might have one child of the normal biological sort. A child who could have spawned thousands of generations of descendants throughout the 3-million-and-change years since he got on the ship. The letter he got from his ex-girlfriend said she was 7 weeks pregnant, and thought it might be his, which means that this must have happened very shortly before he joined the JMC. (Now, they've gotten mail before, like in "Better than Life", but it makes sense that they'd be receiving mail pods out-of-order since they're traveling in random directions out in deep space, hopping through parallel dimensions and actually experiencing at least one entire disintegration of the ship, and mail pod tracking beacons can't be assumed to be that accurate ;) ). Of course it turns out that the child isn't his, and he immediately does the "guy thing" and shuts off his emotional attachment and turns it into disgust at how she slept with "Roy". But we do see this vulnerable part of Lister yet again, for most of the episode.
If there is ever an absolute resolution episode of Red Dwarf, it really should be one where Lister is reunited with one of his descendants (however spacey-wacey-timey-wimey that turns out) so he can get that closure. He's long since given up on "returning to Earth" as the Plan, and now he just wants to be a good Dad.