As I pointed out elsewhere
-- I'm not a mechanical engineer, but this sounds very similar to a problem that the previous owner of my boat mentioned to me, triggered by your comment "lift pump".
The fuel tank on this boat is under the engine and goes way down into the keel. Even at a reasonably high fuel level the small electric lift pump didn't have enough grunt to lift the fuel from the tank and feed it into the injector pump with sufficient pressure, so the engine would idle but do no better.
The solution was to install a day tank into the engine bay and a higher capacity fuel pump (just a Johnson brand all purpose pump) into the engine bay with it to pump 25L of fuel at a time from the main tank into the day tank.
The way you can rule this out as a problem is to fill a diesel cannister with fuel and run the input line from the lift pump into the fuel can, placing the fuel can at different heights (alongside and above the engine) to see what results you get.
Option 2 is just to replace the lift pump but with some engines that's not so trivial.