MMmm..
Depending on how long it sat....
It may need to be pulled apart and thoroughly cleaned out, all oil passages in the block, crank etc, including the pushrods and new lifters.
Old oil/dirt/rust may have restricted the passageways all over the engine.
Or it could be something simple, like the oil pump itself.
I would start with the oil pressure, hook a guage up, drill prime the pump and see what it gets to and pull the pushrods out to see if they are clogged up.
Odds are, if the rods are clogged, the rest of the motor is too.
Dieseling can be a few things..
Timing a bit off, carb too rich, carbon build-up making a hot spot allowing the fuel to burn after shut-off etc.

I would really find out whats up with the oil pressure and lack of flow before worrying too much about running it again. No oil or lack of flow will kill the motor quickly.