You must be a Champion (beat the Elite Four and champion then resume playing), get the [Mega Ring upgrade](https://gaming.stackexchange.com/questions/136624/why-is-my-mega-stone-not-in-the-location-it-should-be/136625#136625) by doing a Battle Mansion event then battling your rival and meeting Sycamore in Anistar City, and then visit Lumiose City again. Looker called me almost immediately after entering the city, and reentering the city will usually trigger his calls to start the next "chapter" of Looker events.