Lisa's mentor on the show is a man by the name of "Bleeding Gums" Murphy. His first appearance on the show is him playing his sax on a brigde at night, which many believe to be a reference to Sonny Rollins. Rollins is a famous and influential saxophonist who got his career started at age 11, is still touring and recording at age 80, and was elected in to the Down Beat Jazz Hall of Fame in 1973. Obviously this reference to Sonny puts Murphy in to a category of phenomenal players. By being a mentor to Lisa, he partially elevates her to that level as well.
"Bleeding Gums" Murphy plays jazz and blues, and even performed a vocal/saxophone piece on TV that Lisa wrote. His support of Lisa helps her improve her skills as well as get recognition for the piece she wrote. An example of Murphy counnseling Lisa about blues takes place in the following conversation:
Bleeding Gums: "You know, you play pretty well for someone with no real problems."
Lisa: "Yeah, well I don't feel any better."
Bleeding Gums: "The blues isn't about making yourself feel better, it's about making other people feel worse. And makin' a few bucks while you're at it."