Lost horsepower on 94 Lexus LS400 after warm up.

Fuel line restriction?

check the fuel filter, if it plugs up this can cause no fuel flow to engine. Also check the air filter and the plugs, and wires, if not the filter. It can be most anything but hope this helps. or it may of went into limp mode, if so call or take it to a garage.

You are on the right track with questioning the fuel pump.
Someone would need to check fuel pressure with a gauge when it fails to start. The pump relay or the pump could be failing.

the best thing to do is to have the car scaned with the diagnostic computer to see what fault codes are stored.
acording to the fault code you'll be able to work out what's wrong with it.
I'm sorry i ca't be anymore helpfull.

I had the same problem with my 1992 LS400. My Lexus mechanic fixed it by replacing the MAF(Mass Air Flow).

This used to drive me crazy when the weather was hot.

play with the dimmer , may have loose contact.

Could be the ECU has failed. Is the Check Engine Light (CEL) on? It should light up when the IGN is turned on, before you try to start. If not, the ECU is not powering up. This does not mean the ECU is dead, as there are relays and IGN switch circuits that route +12v to it. If you smelled something like rotten fish when you lost power, then its because electrolytic capacitors in the ECU have failed. ECUs also have a "limp-home" mode when the engine management circuits have a partial failure.

check the coolant temp sensor very common problem on these cars

put key in door any unlock manually twice, this will de -activate alarm