If the schematic is correctly drawn, the circuit works like this:
When SW1 is closed, all the current passes through Inside Lamp, and through the switch which can be considered 0 Ohm. Outside Lamp is shunted out, no current passes through it. (But it should still be considered live.)
When SW1 is open, the current has to go through both lamps. The lamps are in series. If the resistance of each lamp is the same (this resistance is temperature dependent), each lamp will have half the voltage it should. Probably enough to light them up, but not at full brightness.
If one lamp is emitting light and not the other, it's probably because of a temperature difference, or minute differences in the filaments during production. Both lamps are effectively passing current, but one of them is cool enough that you don't see the glow.
It is highly unlikely that this is how the lamps are supposed to be wired.
I suggest that you hire a professional for this job. Doing electrical wiring when you don't know exactly what you're doing is dangerous. It can lead to the house burning down. Or someone getting electrocuted. It's not somehing to be taken lightly.