I'm pretty sure the fried liver as a whole is not as good as the lolli (6. d4)
Dan Heisman in Chess Life pretty much refuted the Lolli as a winning attempt. Houdini 3 Pro continues 6...Nxd4 7.c3 b5! 8.Bd3 h6 9.Qh5 hxg5 10.Qxh8 e4! 11.cxd4 exd3 12.O-O with about an equal position.
For centuries it has been believed that the main line of the Fried Liver, 1.e4 e5 2.Nf3 Nc6 3.Bc4 Nf6 4.Ng5 d5 5.exd5 Nxd5 6.Nxf7 Kxf7 7.Qf3+ Ke6 8.Nc3 Ncb4 was correct.
Jon Edwards in Chess Life suggested that 9.O-O c6 10.d4 Kd6 11.Ne4+ favors White; I agree. At a fast time limit Houdini tried 10...Qf6, but after 11.Qe2 White gets a big plus.
With 10...Kd7 11.a3 Nxc3 12.axb4 Nd5 13.Bxd5 cxd5 14.Ra5! & White is better.
The key improvement for Black which was played in no games I have found in my Big data base from 2013 is---6.Nxf7 Kxf7 7.Qf3+ Ke6 8.Nc3 Nce7! 9.d4 c6 10.Bg5 Qe8! The Pro's improvement over the book line, 10...h6.
I cannot find any advantage for White after 10...Qe8.