I have a 1985 S15 here for parts that my motor came from, and there is no lift motor in the tank, just the electric one in the engine compartment with a heater.
As my Sonoma originally came with a fuel-injected 4.3, I left the fuel pump in the tank. It doesn't put out too much pressure at the IP, presumably partially due to the thicker fuel it has to pump. It's been pumping it for over 2 years and 40,000+kms, so it doesn't mind the diesel fuel.
Mine too seems to have this cold start issue. It starts for a second, then quits, unless I give it fuel. It will do this for a few seconds, then it is all right. Only on cold starts. I put some of the blame on the fact it has 500,000 kms on it, and no doubt it's a bit tired

. Some day I'll take the time to investigate it. For now, I'm going to live with it.