He's got his thumb in a ring, similar to the two tied around his left arm. The rings were probably favors from his mistress, Anne Vavasour (for whom the painting was probably commissioned).
And no, I hadn't thought of doing one as Obi-Wan Kenobi, but here's a quick one of me as Darth Vader. :-)
According to the Turks' exhibition at the Royal Academy, London, thumb rings were worn to denote prowess in hunting and military matters, which would fit with Lee - (he's my Ph.D. topic!) Any art historian ever heard of this before?