Dave Lister is an alternate future version of Dave Lister of Red Dwarf. He is unique for being the first future version of Lister shown in the series, and has the highest possibility of ending up Lister's true future.
Dave Lister's life lived the same life as his younger self at least until season two. Following this however, it is unclear if he ended up having the same adventures or living the same kind of life his younger self did. What is known is that at the age of 171, he was at his bunk with knowledge of the future echoes. It also appears to have met his twin sons again, or at least had two more children that he named Jim and Bexley, who have had children themselves somehow. While not confirmed, it is possible that ten years later he died (RD: Cassandra).
While not confirmed, it is possible that the version of Dave Lister shown in Stasis Leak, is the same one shown in Future Echoes, just at a further point in his life. This will explain much about the life of this Lister and would reveal the identity of his children's mother to be Kristine Kochanski.
There is an alternate version of this character who is the future version of either Dave Lister of the novel Backwards or the Dave Lister of the novel The Last Human, or another version altogether. He appears due to the future echoes and appeared to be exactly the same as his TV counterpart. However, the difference is that it was Bexley's son who died instead.