Unless someone has a copycat recipe, you can tell your customer, you can make them a lemon cheesecake but you cannot guarantee that it will be the same as Publix's cheesecake.
Do you know if they actually made the cheesecake in store or was it shipped in?
Betty has a recipe at the link below. I don't know if it's the same or not.
http://www.bettycrocker.com/recipes/lemon-supreme-cheesecake/a5e2da05-50ad-4cdb-930e-72abdbef3f78
The customer probably didn't know because most people don't know that instore bakeries don't bake on site.
You may try talking to one of the bakery employees to see if the cake was made onsite or if it was shipped in.
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