Is it possible the Rune could have winded up somewhere or Lazlo is still alive during the period of other Suikoden Timelines? And.. in case he wasn't. Shouldn't the Rune be wrecking havoc in the Island Nations by that time (well.. unless he traveled to somewhere farther of couse.)
I guess another possibility is that Lazlo becomes Lino's heir (Kika suggests this during an in-battle dialogue in Tactics) and ends up ruling Obel and leading the Island Nations, which is usually the right of Tenkai Stars to become leaders of the nations they've liberated/unified.
And maybe Lazlo eventually finds a way to remove the ROP from his body and has it sealed in the Ruins of Obel.
Well the Rune of Punishment rejected Graham Cray when he tried to reclaim it, so it seems happy to be attached to Lazlo's body. So I guess it depends on the rune's mood swings. Maybe as wars continue to break out across the world, the ROP decides it wants to come out of hiding and start going on a destructive rampage again.