I have two small areas of it in my garden. You don't have to mow it, but it still needs weeding (including pulling out grass that tries to grow in it), and it dies if it gets too much foot traffic when wet, or too much shade etc.
So if your lawn is a mess for any of those reasons, I don't think it's the answer, sorry!
It is lovely in the summer when it's in flower though 🙂