In a way, your ratings on Chess.com and Lichess are legitimate – but that's only within their respective data sets. Someone rated 2200, for example, will always be able to beat someone rated 200, 300, and 430 at blitz in their platform. However, their ratings are not as legitimate as a FIDE rating would be for calling someone a GM or IM. You'll still need to get rated by FIDE for that.