LPOP is not making enough pressure to feed the engine and the HPOP reservoir during cranking when hot. Remove the LPOP and inspect it for wear. There are clearances available to measure the pump and determine if it is go or no-go. The LPOP is directly behind the balancer on the front of the engine. New pumps are available from Melling, Ford, International and probably others, I've seen others recommend Melling for this application, I've used them for over 20 years. Be sure to check the front timing cover for excess wear too, If there are any grooves in the machined areas wear the pump gears move, the front cover will need replacement.
Again, these are F-450/550 problems because of lots of highway rpm meaning more cycles on the parts in the same miles as a F-250/350. Just by gearing alone, a truck with 4.88 gears will turn the crankshaft 31% more than a 3.73 truck. A truck with 5.13 gears it's 38% more. If a 7.3 spent 100,000miles in overdrive with a 3.73 gear and a 32" tire it would turn 29,000,000 revolutions, 235k is about 68.2 MILLION revolutions, not counting all the time spent in 1st, 2nd, and 3rd gears where the engine turns far more revolutions per mile, likely enough that a 235k mile 7.3 F-250/350 with 3.73 gears has probably spun the crankshaft close to 90 million times in it's bearings. That means an F-450/550 with 4.88 gears will have closer to 120 Million cycles on the engine. Make sense that the oil pump can wear out?
On the same note, F450/550 trucks with 4.88/5.13 gears should have their oil changed on lower mileage and hours schedules than 3.55/3.73/4.10 geared trucks.
Sent by my right thumb!
The Current Truck (Oct-2013 to Present):
1999 (Early) F-350 Lariat, CCLB, SRW, Black/Tan
7.3L Powerstroke, 4R100, 4x4, 3.73, 37x13.50-18s, '05 Axle Swap, 6" Fabtech lift, GTP38 "D66" turbo upgrade, SCT 4-position chip with custom tuning by me, Straight Piped 4" down pipe through 5" dual stacks, N-Fab full length triple steps, Pro-Tech cab guard and tool box, louvered 5th wheel gate, Hella 500 Fog and Driving lamps, much more to come...
The one I'll miss, (Mar-2009 to Jan-2014):
2000 Excursion XLT 4x4
6.8L V-10, 4R100, 4.30, 285/75-18, 271whp / 388wtq
The one I won't, (Jul-2005 to Sep-2012):
2005 F-350 XLT, CCLB, SRW, 4x4 FX4
6.0L PSD, ZF-6S650, 3.73, 35x12.5-18, 4.5" Lift