What does he think of?

His wonderful, admiring, sexy fan-girls? ;)

I'm sure it has something to do with Lily. Perhaps when they were in the meadow,and he was telling her everything about the wizarding world (ya know, before he hit Petunia with a branch and upset Lily)?

Because his Patronus IS Lily's memory. Remember in "A Prince's Tale" when he cast the Patronus in front of Dumbledore? The "after all this time" and "always"? His patronus is BECAUSE of her.

his friendship with Lily? The first few years? Or the time before Hogwarts?

The day Sirius died?...just kidding. I'd say probably his memories of his time with Lily before going to Hogwarts. The times he spent telling Lily about magic. They would be the few instances where he'd be able to speak enthusiastically about magic, be able to impress her with what he knew and also have her full (possibly admiring) attention on him.

Well seeing as his patronous still takes the form of Lily's, I think it must be a memory of her :) She was the only thing that ever made him truly happy. I'd like to know what exactly the memory of her is though, maybe they did share a kiss at some point? It'd have to be a really strong, happy feeling to produce a patronous and memories of Lily are likely to be bitter-sweet for him.

lol like bri-maries comment XD
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well I think it'd be the memory of lily; I agree with everyone else here :D she was basically the only happiness he ever found in his life.... *sigh* I really hope thats wrong, though

I say that he was thinking about The moments he passed with lily because those were actually the happiest moments in his life and because he truly loved Lily;)

I might just be c
me but I think it's pretty clear that it's Lily he thinks of and that's why his patronus I a doe the same as hers