The lift pump is normally the culprit in cases like yours. There are conflicting stories as to how easy they are to replace with some saying the tank has to be dropped whilst others say it can be done through the access hatch under the rear seat.
Lift pump failures are surprisingly rare on here TBH whereas most car enthusiasts see the lift pump failure as a 406's common failing, and a bad thing
All I can say is, if your happy to have a go then go for it, if not find a decent indie you trust, the fuel lines are supposed to be flushed although some let the fuel filter catch any bits from the pump failure (if there are any bits) apparently you may find metal filings in the fuel filter 'bowl' at the engine.
One more thing, when you set the keys to 'ignition' can you here the buzz of the pump anymore or nothing? if nothing then the pump is dead for sure. Oh and don't crank the engine too much as the high pressure pump won't like the lack of diesel/lubricant.
Welly