I'm the manager of a very successful business and sometimes when I can't deal with a customer and they ask for the manager I'll send them to what ever employee was late to work that shift instead.
You are the manager and yet you don't want to deal with it yourself?
The employee should be punished for their negligence and the customer should understand that I have to run a business here.
You do have to run a business but you are the manager and it's your job to deal with customer's complaints, not lie to them and pawn them off on an employee as if it were a reward to your employee. Dishonesty will lose you customers.
It's fine, It's not lying if only the ignorant ones get fooled by the rouse.
It is giving deceiving information to the customer and creating a toxic work environment.  If you want to have a good business reputation, you should stop actions like that