Answer
The overall resistance decreases. More current is drawn from the source.
Work Step by Step
Assume that the voltage remains constant.
When both bulbs are lit, more power is being consumed because both bulbs are on. Consider the power equation $P=\frac{V^{2}}{R}$. The voltage is constant, so the power increase means that the resistance decreases.
This also makes sense because the lighting fixtures are in parallel with each other. The total resistance is that of the two resistances in parallel, which is less than either resistance.
