Q: Security light and engine light on car not start on 1st attempt

12 equinox 2.4 turns over a little bit when no start intermittently occurs however 2nd try always works. replaced battery, p062f , p015a0 occurs intermittently sometimes after sitting overnight but also after a short drive and attempt to restart. Check engine light along with Security light comes on and goes off by itself without a discernable pattern. Replaced with new AZ gold battery but did not remedy problem as engine light reappears sporadically as well as no start. After a 2 sec break from initial start, the car has always started right up. Sometimes there is a feel that the engine is stumbling or about to cut off and give it a bit of gas to maintain idle on 2nd successful attempt to start engine. Also hear what can describe as light backfire noise in tailpipe occasionally. Tried Lucas fuel additive with no success as well. Chevy dealership said they replaced theft control module & key however car engine and security light came & no start right back on

My car has 124000 miles.
My car has an automatic transmission.