I recently came into possession of a 1990 Buick LeSabre. It has been running off and on for about a year. Today I started it up and it ran fine for about 30 minutes, then I started it up again and it would rough idle then stall. It runs fine when I hit the gas, but once I let off it only runs for a few seconds before stalling.
I'm assuming it'* a fuel issue, but I don't know specifics. I'm not totally savvy with this kinda thing but I'll try and provide information best I can.

Do you want information? Do you have tools? You mention fuel pressure do you have a simple pressure gauge?

Can you keep it running by giving it just a little bit of throttle?