I know you have to go to Lumiose City, but I'v been there a lot of times and Looker hasn't called yet.
You must be a Champion (beat the Elite Four and champion then resume playing), get the Mega Ring upgrade 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.
once beating the elite four and champion, head to kiloude city and battle your rival, he/she will then tell you to go meet prof. Sycamore in Anistar city, speak to him, once he has upgraded your mega ring, head to lumiose city and looker will call you. Also after the looker story you can get into the Sushi High Roller.
I had the same problem without him calling me, no one tells you that part.
Do some battles at the battle mansion in Kilode City. Find Serena/Calem and they will tell you to go meet Sycamore at the crystal in Anistar City. He will upgrade Mega Ring. Then go to Lumiose and walk a bit. Looker will call you after you go to Rouge Plaza and in one of the areas the Looker bureau and complete missions done!
After you beat the Elite Four, go to Kiloude City, face your rival, just look around the town to find her, after you defeat her she'll tell you to go meet the Professor in Anistar, do so then fly to Lumiose, I don't think it matters which section you go to, the after you walk 1 or 2 steps you get a call on the Holo-Caster, this is Looker. And if you didn't know Looker is a spoof of the Doctor from the long-running British sci-fi show Doctor Who, the 10th Doctor is played by David Tennant and if you go to the Looker Bureau before you trigger the Looker event, the man in there states "The tenant isn't here yet." The TENANT. Tennant Tenant see the similarity? Overall he just looks like the Doctor, and he goes by Looker, nothing else, just Looker, the same way the Doctor goes by the Doctor.