Can’t buy a suit in Meltdown because the store is always closed

According to this forum thread, one post says:

Alright, go to Michael's house and go to his wardrobe, pick "full suit" and there should be two of them(grey and blue). Pick either one and then you'll be ready.

Another post in the same thread notes this caveat:

Finally got it to work. I used the same suit as before (the first in Mike's wardrobe) but this time I made sure not to have any blood on my suit from car crashes, shoot-outs, etc. Looks like that was the problem.

This information leads me to believe that any full suit is the correct choice, but you must make sure to keep your suit clean until you talk to Lester.

Go the the wiki and it explains everything.

Can be ordered on a special in-game app after completing Franklin's intro mission. Has to be picked up at the location give on the map. One of the most common locations for pick up is at Los Santos International Airport.

So you have to go to that location. The woman just says she'll have it ready for you on the pad. Not come to you.