what wattage are the light? that splitter is not a good choice you want a heavy duty three way splitter so as to reduce the chance of fire.
the timer and the splitter both have to rated over the culminate # of amps drawn from the lights. so if you run x3 400(3.3 amp ea total amps= 9.9) to a 15amp rated splitter attached to a 15 amp rated timer on a 20amp circuit you will be ok.
also you only ever want to run no more than 90% amps on a circuit, so on a 20 amp circuit, its best to run under 18 amps.