Had this happen on my L-series once—turned out to be air in the fuel system after a cracked fuel line let air sneak in. I'd start by checking all fuel line connections and the fuel filter and bleeding the system. Also, make sure the fuel shutoff solenoid is clicking properly—it’s an easy one to...
Sounds like a voltage drop issue, check for corrosion or loose connections at the battery terminals, ground strap, and starter. if those are clean and tight, your starter solenoid or ignition switch might be acting up.