Will the bright of the bulb increase or still the same in this simple circuit?
You are ignoring lamp 1... In this instance you can consider Lamp 1 as the internal resistance of the battery. 

That is, the current through Lamp2 PLUS the series chain Lamp3/4 MUST be drawn through Lamp1 with an attendant voltage drop across Lamp1.

When you remove Lamp2, less current is drawn through Lamp1. Less voltage is dropped across it, and so more current is drawn by Lamp3/4. Till it rebalances.

In the end Lamp1 gets dimmer and Lamp3/4 get brighter.