Low Voltage DC controlling 120 AC, with Arduino
The canonical answer to this is a solid state relay.  If you aren't switching much power you can use counterfeit Foteks found all over the place on eBay for $3.  This is not a good idea because they are counterfeit, but it is a cheap idea.  

As for the "lights wont turn off in time", I think that will be primarily dominated by the speed at which the lamp filaments cool down.  Mechanical relays can disengage in 30-50 milliseconds.