Does insiufficient fuel supply cause engine misfire?

I have recently been having problems with my Ford Windstar 1996. The engine seemed to misfire regularly on the way back from Vancouver the other day. When climbing or decending down steep hills, the engine seemed to stutter, skip to higher revs and then drop back down to normal. Fuel level was low. Although the engine warning light was already on, diagnostics said Cylinder 4 and 5 misfire.

The car this morning ran fine, no misfires, no transmission issues, like the car was like new. During a service this morning, and having previously diagnosed transmission problems, I changed the trans fluid and found no metalic deposits of any kind. Trans fluid was also good.

I changed the spark plugs and cleaned the throttle sensors. When leaving the workshop the car again misfired and the previously clear CEL came back on, and put the car in Limp Mode.

Has anyone heard of this before. Ive had no issue with the car until I get lazy and run the fuel levels down. Im not convinced that its a transmission sensor issue as its intermittent, with the car always starting from cold very well, and then starting to misbehave later in the journey.

Any ideas?