I think Lana's live performances usually don't impress because she's constantly having to sing over her band, the crowd etc. (granted, SNL was a quiet gig but at that time she was just starting out, she was nervous and since then her vocal strength has increased significantly)
For instance these performances are both stellar, and indicate that she's quite capable of giving the blues genre justice.
I mean I'll agree she's no Nina Simone, but her cover of the other woman was fantastic all the same.