“anyone will do” isn’t a direct reason for wanting to fall in love. It’s more that since anyone will do there’s no previous step before simply falling in love. I don’t know that there’s any sort of separate grammar point on this, since I feel its pretty much the usual usage, just in a slightly different context.
Adding to that, you could probably also translate this something like “I don’t care who with, I just want to fall in love”
から here is used more as part of an expression, but the meaning is closer to “because” than “from” in this case. But it’s still not exactly “because”.
You hear it a lot, especially “いいから”, in anime and dramas.
いいから早速来てよ!
I don’t care/never mind, get over here immediately!
If you were to translate “いいから” literally, it would be something like “it’s fine”, with the implied meaning that “I don’t care about what you were just telling me”. This is a bit different to the original sentence however.
So in the original sentence, 誰でもいいから could be translated as “anyone is fine”.