Applied pressure but couldn't find the way to close it out

4. Ng5 seemed overly aggressive. Instead of hoping he would fall for the 'fried liver' probably should have developed another piece.
Keep in mind when your knight is there the bishop on c1 is guarding him. Queen wouldn't be able to take him.
9. Qf3+ probably would have been just as good as Qh5+, still would have guarded Bxd5 and led to 11. Qf4+ g6 and his king would have been open (forcing g6 a lot sooner, been able to either throw Bxh6 or something else to force it open even more. I can't do the next couple of moves off the top of my head, but it would have gotten you to where you wanted a few moves sooner, without the 'wasted' 13. Qf3.

if you are not sure of a sacrifice and it's consequences, don't sacrifice, look at the position untill you mate/gain matereal/ win by piece play or position/etc...
the Lolli attack is very risky and ends with you having only a queen and a rook for the mate (if black plays correctly), look at the moves made in the game explorer, and memorise them for the next game... and look for tactical opportunities, but also at quick piece developing, witch can be ever more important while attacking in the opening.

Interesting game and thank you. His unobstucted development got you. Xmenace is correct (as you recognized), but I think his combination starts on move 11 and/or 13. Also, if you are shy to sacrifice and I sympathize as I tend to "out-clever" myself with an occasional failed sac, you could have tried 11 Qf7 where 12 Be4# is expensive for black to avoid.

I think 6. Nxf7 is stronger than your 6. d4. At least, Estrin in his book "Two Knights Defence" suggests it. He gives 6. Nxf7 Kxf7 7. Qf3+ Ke6 (The only move or White is just up a pawn) 8. Nc3 Ncb5 (There are other moves as 8. ... Nce7 9. d4 where it gets complicated.) 9. a3 ! sacing the rook for the attack. I played this line a couple of times in the 80's when no one in my club knew what to do (they never played Ncb5 for instance) and I won a few nice games. Usually because Black would find the wrong moves at the wrong time. Look it up in a good book, Estrin's book is way out of print and although it was written in the 50's or 60's, the lines are still good.

One other thing, Estrin on his section on Lolli's move (6. d4), doesn't consider Black's reply 6. ... exd4. He only looks at 6. ... Nxd4, 6. ... Be7, 6. ... Be6 and the main line 6. ... Bb4+ with the idea of 6. c3 Be7 preventing White from playing Nc3. That means that either he overlooked it, or its been refuted (if so why not put it in), or there is something inherently incorrect. If you have an engine put it in and see! In your game I also think instead of Qh5+, Qf3+ is stronger.