If the LP is failing it does starve the HP unit of fuel causing the power loss at higher speed. Replace the LP unit and see how it fairs. If they find metal fracgments because its been driven too long with the LP bot working and the tank has been run low then technically it will need the tank removing and flushing including all fuel lines & a replacement HP unit and injectors.

That is exactly why I never allow my Diesels to run much below half a tank. fuel is the only lubrication for these HP units

Dealer is going to "try" to fix it!!Equipment for testing the L/P pump isn't exactly high tech,a simple pressure gauge and a graduated container will do.ok,maybe they don't have a 'scope,they should have,but come on,I've tested a L/P pump out put on a breakdown with couple of bit of pipe,a compressor gauge and a Coke bottle!not exactly rocket science.and yes the pump then was shot,low pressure and delivery.Dealer is going to try to fix it!!