Problum starting and runs real ruff

My sts when I start it and this is very random it will run so ruff and lack of power it barely pulls away from the curb. If I sit and wait and nurse it trough the motor lag by increasing RPM slowly it will stop missing and run normal. If I start it 10 times in a day it might have the issue 4 times. Every few days when I go to start it if I'm in a hurry and try to rush it when it's missing it will die and then not restart. I do have an engine light on had it checked and it says motor is running lean I pulled the plugs and replaced them and the did look like the motor is running lean.