Why don't my fluorescent lights work after a nearby lightning strike?
They all went out at once? It may be a loss of power to the lighting circuit, or it may be a power surge taking out all the fixtures. If the power to the fluorescents is good, then it's one of two things: 


the fluorescent tubes ($2-5)
the ballasts ($15-25) -- a ballast is an electrical module inside the fluorescent fixture which controls the power for the tubes.  Fluorescent tubes take specially regulated power, not common mains power. 


It's more likely the ballasts than the tubes, but the tubes are easier to swap.  There are Q&amp;A on here which discuss at length identifying and changing ballasts. 

Fluorescent tubes are now very good, and no longer give the green flickery sickly looking light they once did.   If it is the ballast, however, you may want to price out switching to LED replacement fluorescent "tubes".  Make sure to get direct-wire types, not the kind dependent on ballasts.