An observer might be forgiven for thinking that she's ashamed to face him because part of her feels remorse as regards her morally repugnant act of rewarding a lying thief who flattered her but, much like her mother, she tends to substitute moral indignation for actual morals. Much as Elly will never apologize for what Kortney did to April, Liz is never going to want to feel guilty about Jim's harmonica...especially since he kind of always scared her as a child.
You see, I never had any sort of impression that Jim responded the way Lizzie wanted to when she pretty much flirted with him the way she does with her sick freak of a father and that made Lizzie wary of the old boy. When you base your identity on trading on your looks and someone doesn't buy what you're selling, you don't necessarily like this person. This inability to quite get what she wanted as a child explains why she sat in cars waiting to get away from the smell and sight of scary old people who die when she gets to know them.