Isolation transformer Confusion
The ground symbol is misleading. The lamps are connected to each other. This completes the circuit from one side of the transformer to the other. This illuminates both lamps in series. 

If only one lamp is connected then nothing would happen. 







simulate this circuit &ndash; Schematic created using CircuitLab

This is what the effective circuit looks like. 

As far as the voltage after the transformer, you have to pick a reference yourself. But now you only have two choices. One wire is the reference and the other is hot. The hot wire goes +230 then -230 then +230 when compared to the reference.