Actually he wasn't waiting for his lady. He was waiting for his friend.
You're right. The lyrics say, "I'm not waiting on my lady". Nevertheless it's a pretty good song. Didn't care much for the Stones after the Seventies but they did good with this one.
Sticky Fingers, Exile On Main Street are my two favorite Stones albums, closely followed by Beggars Banquet and Let It Bleed.