How do I treat this "lamp" to find power dissipated?
Use the power equations, P=I^2*R and P=V^2/R, you can use either one.

For the lamp, if its on, the equation would be \$P = V_{lamp}^2/2\$

You can analyze the circuit like normal to find V_lamp

Another way you could do this is if you find the current and the voltage through the lamp, then use the equation P=I*V