FUNNY STORY TIME
Sonic X-treme never even saw the light of day, so no. It is highly likely that idea for Lost Worlds came from it, however, seeing as how there appears to be elements from X-treme in Lost Worlds.
Sonic X-Treme almost
got finished, and some years ago a developer discovered a build that he had burned on CD-R. Anyway, he sold it off to the top bidder to the tune of somewhere around $5000 -- so he could have this game all to himself, and if he was feeling generous he might share a screenshot or two with everyone else not wealthy enough to waste that much money on a prototype.
Then a few months later another CD-R copy of this exact same build turned up and the guy simply released it for free on the internet, effectively rendering that idiot's purchase as completely worthless.