Make it so in later levels, it's possible to pick up something that acts effectively as an extra life.
There can only be up to three of these in the world, perhaps one sphere away from the boss level.
Lore can be along the lines of "This Temporal Paradox Generator quantum-entangles with its past self at the moment of passing through a hyperspace portal. If it is destroyed, it causes the destruction of its past self, which creates a temporal paradox - all events leading up to its destruction are erased from the timeline. To all intents and purposes, time replays from the moment of its entering the last hyperspace portal it passed through, with only one difference - the Temporal Paradox Generator never existed."
The mechanic would be that when you're destroyed, if you have one or more of these in your inventory, it forces a game reload (which would be from the entry of the last portal) instead of deleting the player's save - and one of the items is itself removed from the inventory. Basically a controlled method of save-scumming, as an integral game mechanic, and with references to traditional arcade-game multiple lives systems.