Could recent electrical work cause lights to dim when A/C turns on?
Find out what the A/C guy did.  I would guess he did something which improved the performance of the A/C system, so now, instead of the motor nearly freewheeling against little load, it's having to hunker down and really work.  The increased amperage is "bringing to the surface" a pre-existing problem with wiring, probably between the sub-panel and the supply. 

I would now measure to see how serious the problem really is.  It may not be worth worrying about, it may just be over-sensitive bulbs.  

You can mask the symptom by buying modern lamps.  Any multi-voltage rated LED (typically 100-240V) or fluorescent tube ballast (100-277V) will ride through voltage sags.  Avoid the cheapies (Feit, Utilitech, Lights of Amerchina, and CFLs of any make; you will not be satisfied with their long-term performance, and they will give LED a bad name.)