What's weird is that the game says "possibility" and "backup plan". If it were set in stone from that Lavos's perspective, wouldn't the possibility be a certainty and the backup plan a "plan B"?
Simple uncertainty? Lavos saw a future, had no idea how that would come to exist if he was alive, so he concluded that something bad must have happened. Unsure as to what, he did what he could to attempt to radically change the timeline...
Which means that Lavos presumably either doesn't know about TTI, TTI doesn't exist, or he didn't figure the future was the result of Time Travel.