I created an gaming platform few months ago, but it’s restricted to Polish people. I search for somebody, who help me translate it into another language.
Maybe integration with lutris instead? If we integrate my gaming platform with lutris, lutris community could earn cash. How? My gaming platform is restricted to older games and user may turn on cryptocurrency mining. I earn cash thank to that and user will receive coins to get new games for that. I think, I could allow lutris to earn some percent of money from users, who use lutris while play.
What do you think?

…And that’s all the info you’re going to give? You may want to provide a link to your website or something, to show what you’ve got (I mean, why wouldn’t you want to?)

I’m guessing you mean Lutris dev team, because community = users.

AFAIK Lutris team doesn’t get any profit from the project other than from Patreon. Although you can request the integration from them on the project source page (create an issue with title like “Request: integrate with [platform name]”), and maybe support them on Patreon (or use that Sponsor button on the project page, I’m not quite keen on the matter). Though I’m not sure if they’ll be willing to spend effort on integrating with a platform that’s not widely used (at least at the moment of integration); the focus for non-profit projects such as this tends to be on what [a decent percentage of] users would want to have (and you haven’t mentioned much about that).

Basic advice: start from making an official English version, then you’ll have a majority of Internet denizens joining up from the start (well, as long as they’re interested, anyway) since that’s the de-facto global language; and then it’ll be much easier to find someone willing to translate to any particular language from it. As for how to get there – the simplest way would be to make a poor quality translation (by hand or with Google translate), as a separate file or maybe some form of a beta release (a bunch of sample HTMLs if we’re talking about a website, for example) and ask someone to proofread it and help fix translation mistakes (they may need your help to figure out what’s the intended word in places where translation quality was too poor); that way you can get a proper translation without the need to look for someone who has good grasp on both English and Polish (thus, easier to find someone willing to do the work).

My opinion is that providing a translated version for your mysterious gaming system would give a large push to its popularity… And that maybe you may want to at least get there first, before discussing any collaboration with a general-reach opensource project.
Then again, I’m not a part of Lutris dev team, so it’s just a passerby’s opinion.

Only language I support is Polish. Shop currently doesn’t support to pay in cash and each game available is for free, but mechanism to pay in coins are implemented. Users could get coins by playing, where one’s computer gather cryptocurrency. Because computer is used to calculation of cryptocurrency, I decided to public only simple games.

Yes. I mean lutris devs.

I’ll be honest, the default theme is horrifying. It looks barebones (the 90s design, with nonexistent text padding and scrollable areas), and colour contrast in most places makes my eyes bleed. The other one looks better (although some issues from default theme are retained), but I only found the theme switch by accident. Not to mention that the game selection is severely lacking, to put it lightly.

All in all, this will need some serious work (and active promotion) for users to get any interest in it, let alone to have any profit worth mention (regardless of which language they speak). At the very least they should get some decent incentive to start playing (and I mean get “now”, rather than “at some future point, probably”); otherwise they’ll just look for another place to get games. And, yes, fix the site design so that it at least doesn’t look like a proof-of-concept alpha version made overnight; just one look at this index page is guaranteed to make most users leave the site immediately.

(Also, I’m not a specialist, but maybe you should discuss your terms-of-use with some lawyer… thoroughly. And I don’t mean the part where the word “Regulamin” is repeated four times in a row.)