Definition
A lift pump draws fuel from the tank at low pressure and delivers it through the filters to the injection system, and is separate from the high-pressure pump that supplies the injectors.
Every diesel fuel system has two pressure stages. The lift pump handles the low-pressure side — tank to filters to injection system — and may be mechanical, driven off the engine, or electric.
Why owners care about it
It is the pump you operate when bleeding air after a filter change, either by hand lever or by switching on an electric primer. A lift pump that has failed or is passing weakly produces exactly the symptoms of a blocked filter: an engine that starts and dies, or that fails under load while idling fine. See starts then stops.
Because it is on the suction side, a leak here draws air in rather than leaking fuel out — which is why an air leak can be invisible while causing repeated stalling.
Where you meet it
In the bleeding procedure, on the fuel system diagram in your manual, and in the diagnosis of fuel starvation.