“have (got) someone or something covered”

This is an informal expression and it can be used in several different situations:

- to do or provide whatever is needed

- to take care of everything

- telling someone not to worry about anything.

 

If I say that I’ve got lunch covered, it usually means that I will pay for the lunch (to cover the cost of something).

I can't work today because I have the flu. Don't worry, I've got you covered (I'll work for you/I'll do your work)

It means they can make you lunch.  To have something "covered" means it will be all taken care of.  If you say, "I need someone to photocopy this for me," and I say, "I've got it covered," it means that I will do the photocopying for you.

I had my washing machine repaired.
----> I asked some mechanic to fix my washing machine.  (The key note is  my washing machine was repaired)