I agree with others that both names are lovely. They also sound quite literary/artistic (maybe I’m thinking of the book Lolita? But I don’t think most people would make that association – I studied literature at university). My sister’s niece is Lola, and she is a spunky and spirited girl from Madrid, Spain. To me, it’s cute, fun, and artsy, and I love the dramatic long O sound.
Etta is actually a nickname my husband and I are considering for our upcoming baby girl Odette, so I may be biased 
Etta, to me, is soft-sounding and (perhaps more subtly) continental European, like a form of Greta. Both names strike me as literary.
I agree with the others that if Lola really speaks to you, go for it! I’m sorry it’s been received negatively. It’s not at all unusual and seems like generally a safe and perfectly respectable choice in today’s diverse and oft adventurous baby-naming world.