You have to beat all Master Rank Contests to face off with Lisia in a Contest.
Once you are up against her, I suggest using this Gardevoir moveset to beat her:
Gardevoir @ Gardevoirite
Max out your Cleverness.
Go for Calm Mind to get yourself pumped up, before using Stored Power. If Lisia mega evolves her Altaria and gets all the hearts, use Draining Kiss to copy her heart count. Use Destiny Bond on the last turn.
This is in the Cleverness category of the Contest Spectaculars. Hope that I helped!