I'd rather play 4...Nf6, and you should learn the panov.
Two Knights defence ? Well, the most interesting lines for White are definitely with 4. Ng5, not 4. d3, and this leads to the Fried Liver attack.(and by "Italian game", I meant 1. e4 e5 2. Nf3 Nc6 3. Bc4)
So what do you play after 1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. Ng5 ?
4...d5 5.ed Na5!
4...d5 5.ed5 Na5, as in the previous post, although the "bad" 5...Nxd5 is also playable.
5... Na5 leads to an unclear game, though White will be a pawn up.
5... Nxd5 seems very dangerous after 6. Nxf7.
Wrong. 5...Nxd5 6.Nxf7 is actually OK for Black, although the position is quite complex. The only real problem is the Lolli (6.d4!) where Black is somewhat worse, but he can pull a few rabbits out of the hat.
5...Na5 is a cleaner solution, and after 6...Bb5+ Black can pick either the ambitious 6...c6, or the solid 6...Bd7. IMO both are perfectly adequate.
The Lolli is indeed the best option after 5.Nxd5.