If you use Arduino directly as a switch for AC supply then this is not going to work although it would cause a catastrophe because 225V across Arduino's pins are going to damage a lot.
So the solution is to use Isolation of two Arduino and the Lamp.
Isolation can be done as @yogece said using a Relay and Relay driver.
Relay is kind of current operated switch i.e. if sufficient amount of current flows through Relay coil then a switch will be CLOSED otherwise remains OPENED. The current driven by a typical relay at its rated voltage is between 25mA to 70mA.
As the I/O pins of Arduino can provide maximum 40mA current (According to ATMEGA 328 Current Specifications) it is not a good idea that you directly connect it to a Relay and if you do so it may burn the Arduino. This is why you need a relay driver.
A very simple Relay driver can be made using a transistor.
This article can help you understand very basic Relay driver
Here is a typical circuit,
simulate this circuit – Schematic created using CircuitLab