Thanks everyone for your helpful insights. I'm going to send the professor a follow-up e-mail, which I wouldn't have had the nerves to do if it weren't for your comments.
I wonder what a "No, I don't think I should write your letter" response would look like. I have 2 solid letters based on research experience from two different labs, but I'm struggling to secure the third letter, which will probably end up being a "She got an A in my class but I don't know know her super well," anyway. Unfortunately, most programs require 3 letters, and want 3 strong ones.
One additional question: Have most of you gotten all 3 (or more) letters from professors in your field? Does it raise a red flag to have one of your letters from a different academic department?
Thanks!