My 2007 Nissan Frontier will not start. I started the truck this morning and it started fine but soon loose power and stalled or shutdown. I went to pump the lift pump over the fuel filter but nothing

This morning I started the truck and it struggled a bit to start but started up then soon after faded and shutdown. I went to pump up the lift pump over the fuel filter but it still will not start.
The day before it started and shutdown soon after as well, however, after several turning of the key it finally started and kept up. I drove to work yesterday but after about 1 hour I went to start it again and the same thing happen. it start and then shutdown, then took be several turning of the key before it finally start up. Once I start for the second time it never fail again and will keep me going all day once I don't turn off the engine.

I was told it is lift pump issue because the fuel in the filter back flow after the engine is in park.

Nissan Frontier 2007 model – YD engine, Japan made – export to Jamaica
4X 2, Di 2.5 turbo diesel

Can you tell me if this may be a correct assumption?