The original Super Mario Brothers has a surprisingly in-depth system for hidden 1-ups.
On the first level of each world, 1-1, 2-1, etc, there is a hidden 1-up block that has a number of conditions for its appearance.
If you warped to the first stage of the world, like using the famous 1-2 or 4-2 Warp zones. The hidden block can be found. If you didn't use the Warp zone, then you need to collect most, if not, all of the coins in the previous world's 3rd level. 1-3 for 2-1, 2-3 for 3-1, etc.
1-1's hidden 1-up always appears, there is no prerequisite for that.
Now! If you get to the stage and have met the requirements but die after getting the 1-up, it doesn't reappear!
Honestly. I feel that is a lot going on regarding this mechanic, way more than it is absolutely necessary!