I think you're looking for an app that's a checkmate above the rest... literally! There isn't one yet, but I found something similar called "Chess.com" which has a feature called "Tournaments with Prize Money". It's not exactly like Lichess, but it does have the potential to get you richer.

However, there is another app called "Twitch Roulette" where the winner can take home some Satoshis (Sats) from the loser. The catch? It's more of a charity event and for good causes only

But if you're still looking for something that'll make you go all-in for Sats, I'm not aware of any app that's currently doing this exact thing.

Keep in mind, though, that there are some online chess platforms that allow players to compete for real-world prizes. These events usually require a larger commitment, but hey, who knows? You might just become the next chess champion and Satoshis richer