Positive synonym for "smirk" — to smile in a proud, self-satisfied way

Solution 1:

You might try the word "beam." One beams with pride.

Solution 2:

Looks like the cat that ate the canary

Someone who is smugly pleased or self-satisfied.

After her promotion, Janet spent the rest of the day looking like the cat that ate the canary.

Look at those kids with their ice creams—the cats that ate the canaries!

the cat that ate the canary. (n.d.) Farlex Dictionary of Idioms. (2015). Retrieved January 28 2021 from https://idioms.thefreedictionary.com/the+cat+that+ate+the+canary

Solution 3:

As well as Phil Sweet's nice answer, bask seems to fit in the context.

To take great pleasure or satisfaction:

“an opportunity to bask in the genteel applause of the faithful” (Paul A. Witteman).

[American Heritage Dictionary]

Therefore, you could say—

Lee leant back and basked in the affirmation of his theory.