Players will be able to invite Giovanni as a guest to the lodge if they've been able to team up with 5★ Giovanni & Mewtwo. Giovanni & Mewtwo can currently be acquired by completing stages in the main story's Legendary Adventures.
Giovanni was first teased to fans in posts showing a silhouette of the Giovanni Plushie item that players will be able to acquire and decorate their Trainer Lodge with after befriending Giovanni.
The addition of Giovanni to the Trainer Lodge should perhaps come as no surprise, considering that the Team Rocket Style for the Lodge was added to the Lodge Exchange earlier this month on September 3rd. Players who have not yet unlocked this style can receive it by completing the Final Chapter of the Villain Arc.