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 control 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.