Well, personally (and it might be considered a bit cliche) but I always saw a dog as his Patronus. To me, an person's Animagus form and their Patronus form have strong ties to the individual's personality and such, and at the very least, Book 7 has McGonagall's Patronus form the exact same as her Animagus form. (She casts some Patronus spells in the Battle for Hogwarts, if I remember correctly, and they're her tabby cat form.)

However, the idea of it being the lion is interesting, though I also, personally, see him as having a bit more of a Slytherin side than some fan fic writers want to show him as. So many want to take away ALL signs of a Slyth from Sirius, when in reality, if you at the very least look at some of his character, there's a lot of Slytherin aspects to it.

But then again, I've always been of the idea that Slyths and Gryffs have a lot more in common in terms of characteristics than they actually admit, and the two Houses have plenty of members that share them (Harry, Sirius, Snape, to name a few right off the top of my head).

But no, in canon, there is no CLEAR definition of what Sirius's Patronus form is (the books never have him casting the spell).