Hi Sandeep,
I’ve used a SIM900 based module, and by mistake I was using a 3.3V power adaptor. Still it was giving me response when I send AT comands !
But not able to make a call or send messages.
Since you are using two seperate power supply, the ground should be properly shorted together and the two power supply should not in anyway affect each other. Just make sure using a multimeter that you are getting 5V at the output of the regulator ICs in both your development board and the GSM module.
Post your LCD code, I’ll try to figure out if there is any bug in it.