I screwed up this rook endgame!

It must be totally winning. What can I do better!?

I've attached my post-game ideas at the bottom.



35.Rc2
To go to c3. This is obviously the wrong idea, its so passive. But I used 4 minutes here and other plans had issues. I want to support a c5 or e5 push to trade off their pawn and pass mine, but can't at the moment. Playing for activity with Rf2-f8 didn't seem to give me enough. And I can't hold the position because the black king will enter on the kingside.

49.Re4
d5 instead isn't clear to me. Perhaps Ke2 is better, but I thought I could make progress without allowing kingside counterplay.

58.Rxf7
By here it's probably a draw. For whatever reason I couldn't find better continuations.

The rest of the game was more or less us goofing around.

I've added some quick thoughts here below.
One mistake that quite a lot of players make in rook endings is that they want to protect every little pawn.
You (plural) have to learn that in rook endings not all pawns are equal (Passed pawns are more equal than other pawns. Advanced passed pawns even more), and it is fine to sacrifice a pawn or even two or three just for the higher goal : Promoting a passed pawn or checkmate.
My impression is that the rook ending was better for white but not that easy to win.
It seems to me that white had to activate the king, go for the d6 pawn, and give up the h pawns. Then the c (or d) passer will likely win for white.

Thank you! Excited to dig into all these ideas.

I Think that your move 35. Rc2 is good, and better after the mistake 36...Kh5? because this is not the best position for the black king: For example: 35. Rc2 Rd1 36. Rc3 Kh5? 37.e5! dxe5 38. c5 Rb1 39. c6 Rb8 40. Rc5! (you can see the bad position for the King, cause you will take an important pawn and keep the strong "c" pawn for the victory) 40...f6 41. d4! in order to d5..d6... running so fast to the victory. Best regards, JOANDESA.

Good idea master JOANDESA, so it's very clear that the advantage for Lambert is 03 pawns against only one ("c", "d" and "e" pawns vs "d" pawn black) and the rook is in back side, pushing!!!. How do the victory this advantage? reading the last message.