I assume that is the leakage current.Due to the potential difference between both the grounds.
check out these:-
1.Instead of directly shorting both the grounds,connect both through a ferrite bead or an inductor.
2.At the Vcc point of the LCD,connect an electrolytic capacitor and an MLC (multi layer ceramic) parallely.Connecting a similar pair at the Vcc of the whole uC board is also suggested.
3.Hope star grounding is not taken care in your uC board.If so,short all the ground points to a common point with a wire and then short this wire to the analog board ground
This is my assumption.I am not sure,anyways check it up and let me know.