Lyric discussion by sarcasmorgazm 

Cover art for Lady lyrics by Regina Spektor

just expanding on the previous comment

this song is indeed about Billie Holiday

She had an album/song called "Lady Sings the Blues"

"lady lights a cigarette, puffs away, no regrets takes a look around, no regrets no regrets stretches out like branches of a poplar tree says "I am free", sings so soft as if she'll break"

"No Regrets" is the title of a Billie Holidaysong

the part about the poplar tree is a reference to one of Billie's most reknown songs "Strange Fruit"

I simply looove this song, and Billie Holiday