Above you can see that, the max voltage is 20V, recommended max is 12V, but you can use relays to control higher voltages and lamps.
You can [u]control[/u] 54 pins. That means you can connect 1 or 10 lamps on 1 pin and turn them on and off simultaneously (in the same time).
in a glance, if you become more specific about those lamps maybe i can help you further.
Max I/O per pin is 40mA. Total max current of the Mega2560 is around 200mA. So it depends on how much current your devices draw. Generally you'll need a transistor connected to the I/O pin to drive a load.