Said mod allows players to become a Time Lord, but Time Lords have two hearts and different lungs, and when they die, they regenerate (can do this 12 times in their lifetime) which repairs their body.
Maybe cyberware could "eject" the cybernetic additions (robotic arm, etc.) and have a new arm replace it upon regeneration?

In the lore, the doctor respawns in a new body, it's not a repair per say. Existing configuration allows to choose if cyberwares are kept or dropped upon death for all players. That mods needs to actually trigger the death related Forge events.

It does not trigger the events unless the player cannot regenerate

Sounds like a bug in the Regeneration mod to me, hence closing.