1996 Ford Contour Engine Sputter

Hello,
Currently I am having a problem with my Contour where the engine sputters when both idling and accelerating. Sometimes it takes time to start. For example when I try and start it it will turn over fine but will die if I do not apply gas and continue to do so for about a minute or so. After that it will then idle without dieing but will sputter a bit. The sputtering greatly increases when I apply gas during acceleration. If I apply gas while in neutral it does not do it nearly as much as if I'm in gear. It has a brand new fuel pump and fuel filter. New plugs an plug wires. And also brand new ignition coil (although the plug into the on the side that provides it with power is old and wiggles around a bit) I had a mechanic check it once and he told me it was my "ignition control module" but it is my understanding that Ford stopped making these cars with that module separate in 1996 and it is no longer its own part. It is now part of the power control computer so I'm not sure if that truly is the problem. Also I would like to note my check engine light is on with a code indicating my engine is running lean currently even though I have a brand new O2 sensor. What could my problem be?