How to turn LM2577 on/off?
The problem here is that it is a boost.  So, if you were to just turn off the LM2577 somehow, there would still be Vin on the output.  You will need to use a P-channel FET to turn off the input voltage to the whole boost circuit.  

Something like this could work.  

  

As long as Vin is more than 5V and less than 10V the FET should switch correctly.  Of course, now you have to explicitly turn the boost circuit on by applying ~5V to "On" .