2001 ce lancer miss fires under acceleration(at its worst in second gear) but idles fine..any ides?

Check to see if #1 &4 use a common coil pack. If so, = likely culprit.

Some general thoughts - -
when you try to accelerate, a couple of things happen. The engine shifts sometimes, and you put it under a load unlike when it is idling.
Is it possible a wiring harness or a hose is moving when you accelerate ? Is it possible the fuel pressure or ignition module is not good enough to handle the engine under load ? Is the EGR opening early or something causing a vac leak and a lean fuel mixture ?

Sounds like lack of preventative maintenance

Spark Plugs every 3 years or 30 to 40,000 miles

You may have ignition coils failing

Clean MAF Sensor

Replace any O2 Sensors over 100,000 miles

Gas filter every 3 years

hi could be any thing faulty plugs timing out ignition problems does it do it in any other gear does it do it when not in gear and just reving up to same revs as the miss eg back fires not a lot to go off

Check the battery cables. I had the same issues with my 96 tacoma, The battery cable connection at the battery can be cranked down but still be loose. Hard to explain, doesn't make sense, but just check it out.

A variance of 20 PSI indicates a problem.

Have you made sure your getting spark on every cylinder from the coil pack?

Sounds like you have a leaking cylinder head gasket

the idle controls could be the problem

Sounds like a plugged catylic convertor. You might check with a GM dealer to make sure if it falls in the Special Policy coverage to get it replaced under warrenty, it has to have less than 120,000 miles on it though.