Lasciare stare means leave something alone or don't change something. http://www.wordreference.com/iten/lasciare%20stare
They mean two different things. For example, there is a delivery of ice to the grocery store. You say Leave the ice here or there. You are in a restaurant and your children are taking the ice out of their sodas and playing with it making a sticky mess. You could say "leave the ice alone" or "leave the ice in your glasses"
A memory hook that may help some: "Lasciate il ghiaccio" would mean "Leave the ice [behind]" implying that you "let it go" ... think of Anna asking Elsa to leave her ice palace. "Lasciate stare il ghiaccio" implies "Do not touch the ice" like in Elsa telling Anna to not play with her ice palace.
It's an expression, here are some examples: Bene, ragazzi, lasciate stare.
All right, you know what, guys, forget it.
Ok, lasciate stare... faccio da sola.
Okay, forget it. I'll do this alone.
Penny è nella mia... lasciate stare.
Penny's incepting my... never mind.
Andate a giocare con qualcos'altro, lasciate stare la carne!
Go play with something else, never mind the meat!