Current flow with two voltage sources
V2 is completely irrelevant to Light 1.  Light 1 is connected accross a voltage source, so we know the voltage accross it by definition.  The current will be V1 / Light1.

Furthermore, Light1 has no effect on the current thru V2.  The current thru Light2 is (V1+V2)/Light2.  Since V2 and Light2 are in series, that is also the current thru V2.

Note that V1 doesn't show up anywhere in the equations for current thru Light1, and Light1 doesn't show up anywhere in the equations for current thru V2.  The two have nothing to do with each other in this circuit.