I haven’t touch Laravel recently. I hope my idea will help you.
First of all, in general you can’t run Laravel app using of WordPress’s wheel because of differences of mechanism and structure for each one.
Second, let’s think that you have two domains and one points wp and another points laravel app. Then you can set redirect wp’s /store page to laravel app’s domain.
Third, if you are an advanced laravel user, you might be able to point public folder of laravel app to your wp’s store folder. But what’s the benefit of this instead of using 2nd idea.
Fourth, how about making web app and that uses Laravel’s api? I suppose this will be good solution.