Dave Lister is an alternate future version from an alternate timeline that presumably no longer exists.
Three years after being put into stasis, Dave Lister uncovered a photo of himself somehow married to Kristine Kochanski, somehow taken before the accident. Using a stasis leak, he was able to travel back three weeks before the accident and reach Kochanski at the Ganymede Holiday Inn, only to learn that she had married himself from five years in the future. After this, he returned to his time along with the Cat and Rimmer. RD: Stasis Leak
Five years later, Dave Lister found a way to travel back in time to some point before the radiation leak that wiped out the crew and when his younger self arrived. There, he began a romantic relationship with Kristine Kochanski that resulted in their marriage. While at the same Inn, he encountered his younger self and had the same conversation as before from the point of view of his future self, before his younger counterpart eventually left.
However, the younger Lister's destiny was somehow derailed into a new future within the five year gap separating the two, causing this Lister's version of history become an alternate timeline. Presumably, this was caused by the huge paradoxes and time traveling adventurers the younger Lister experienced. It is unknown if this caused this version of Lister to stop existing.
It is unknown what happened to Lister later in his life, but it is entirely possible that he eventually became the future version of him that he encountered as a future echo. It is also possible, though unlikely, that he became the evil future version of Lister who possessed the time drive, which would explain how this Lister was able to time travel in the first place.