I was completing this lesson: https://www.chess.com/mentors/view/7230.
I finishes by saying white wins. However I simply cannot find a winning line. Also I tried the analysis and it showed draw. Is that a mistake in the lesson?
No, I think the lesson is correct. The endpoint assumes you understand a basic concept of king and pawn endgames-the opposition. The position of the king's separated by one square will force black to give way to White's king, which will then win black's pawn and be able to promote its own pawn and win.

Rather than attempt a full explanation, I will look for an article to explain it to you.

I was completing this lesson: https://www.chess.com/mentors/view/7230.
It finishes by saying white wins. However I simply cannot find a winning line. Also I tried the analysis and it showed draw. Is that a mistake in the lesson?