If you save before opening chest and then open and find a Helm, reloading will always give you a helm in that chest -- If you open that chest after reloading, before opening anything else.

Each time, the stats of the helm will be random. You can re-roll the stats on the helm this way, but it will always be a helm.

However, you can alter the behavior by opening a different sequence of containers before the chest after each save. The same sequence will give you the same item type.

You can see the same thing with Lucky Find.

If you save before checking a room with 10 containers and get a lucky find on the 6th, for a Ring, you will always get a Lucky Find in that 6th container of a Ring, if you check in the same sequence each time.

If you use a different sequence so that some other container is your 6th that you check you will still get a lucky find that new 6th container, but it will be for some other item, like a Glove. This new sequence will always produce a glove when you re-load.