I consider romantic/sexual attraction different than the ability to tell if someone is good looking or not. As you experienced, it's very possible to be attracted to someone without seeing what they look like at all. Whether someone is good looking or not can influence your attraction to them, of course, but in any case, I agree, attraction is complicated!
I just know that the definition of lesbian I have always heard is, not being attracted to men at all. If you would still consider being in a relationship with a man, I'd suggest you identify as bi. There are other labels that encompass being attracted to multiple genders too, like pansexual, polysexual, or omnisexual. You may want to do some more research on those, if you're questioning.

I'm bi, and I'm way more attracted to women then I am men most of the time. It's perfectly normal for bi people to have a preference.