Lissie greets fans at the start of Sunday’s performance at the 9:30 Club.

One spin of last August’s Catching A Tiger demonstrates that Lissie is a girl worth knowing. It would be easy to think, given the emotional rock-country roots of the album, that dragging Kid Cudi (and occasionally Lady Gaga) along for the ride would be a disastrous detour from success. On Sunday at the 9:30 Club, the Illinois native did just that, and proved her mystifying range to be one of her biggest assets.