This is a wonderful, fun non-hardcore puzzle game hiding underneath poor decisions, most notably the lives mechanic. It gets in the way of playing and exploring in a painful way.
The jumps can be quite tricky thanks to controls (try to leap out of a deep pit) or subtle bugs (you can easily jump on the stairs in a wrong way), so the deaths feel unfair more often than not, and usually dropping you at the beginning is a lose state anyway.
Otherwise, it's fantastic. Some of the levels are flexible enough that you can skip some sections if you're keen enough, and sometimes you can avoid using a key, carrying it to the next level. Those moments are great.
So my suggestions are, to players - shamelessly use an emulator and take a save state at the beginning of each level, and you'll have twenty levels of real fun,
to author - drop the lives and score and don't get in the way of playing. Add a level selector and count the number of steps taken perhaps - speedrunning this and trying to improve the scores THEN would be amazing. Then this might turn from "can't get through first levels reliably" to a beloved game for ages.