When you die on a run, you will lose a portion of the Lucenite you collected. This is known as the Death Penalty. You can see the exact amount you lost in the Run Summary displayed on-screen and in the Wrist Computer after returning to the Passage.
Note that if you manage to safely return to the Passage via one of the teleporters scattered throughout Carcosa, you will return to the Passage with all your collected Lucenite.
By unlocking certain nodes from the Armor Matrix, it is also possible to reduce the Death Penalty.