An otherwise good running engine will almost always backfire if 'slightly' lean, it'll just quit if its 'way' too lean. 2 and 4 stroke doesn't matter. Surging isnt uncommon either depending on the carb. This has been my experience even on engines with adjustable timing like outboards and fixed timing lawn engines.

Other parts of the country with different climates will see slightly different behavior.

My philosophy involves starting with the easiest fixes first. No need to jump to replacing ignition components right off the bat other than spark plugs and fresh fuel.