>>39728161That's not what we're talking about. OP's pic says ユウリ, Hepburn romanizes that as Yuuri, Nihon Shiki romanizes that as Yūri. You could, using Nihon Shiki as reference, "translate" that as Yuri, skipping the vowel extension entirely for whatever reason similarly to Tokyo, perhaps ease of use for the English speaker, but that's still not 100% accurate to what it originally was, and in this particular case creates confusion. ユウリ is not 百合, but "translating" ユウリ as Yuri makes people think the name is meant to be ユリ. There's a reason why the vowel extensions are noted in romanizations.
tl;dr No, her name does not mean Lily/Lesbianism.