After 1.Kg6 Ke7 2.Rd1 Kxe6 3.Nc8 Rh6+ 4.Kxh6 the puzzle is marked solved. But the engine now shows the move 4...g4??, which after 5.Kg6 is a mate, while 4...Rc3 would "only" be a losing endgame.
http://en.lichess.org/training/45511H_Badorties, you're correct, after 4... Rc3 it's just a hopeless endgame. That's ok, not all puzzles end with checkmate.
The real problem with this puzzle is that I tried 1. Kg6 Ke7 2. Nc8+, which transposes to the official solution after 2... Kxe6 (or leads to checkmate). But lichess only accepts 2. Rd1.
Many lichess puzzles are flawed. We can only downvote them. And it's ok because it's a free service.