Yes your liver can heal itself from cirrhosis as long as the cirrhosis of the liver is not too bad.
If the cirrhosis of the liver has progressed too far then the liver may not ever heal.
Most times when you have cirrhosis of the liver the cirrhosis of the liver is slow and gradual as it progresses and if caught and treated soon enough you may easily recover from the cirrhosis of the liver.
The longer you wait and the further the cirrhosis of the liver progresses the less chance you have at healing the cirrhosis.
However there is no cure for the disease cirrhosis of the liver but treatments can help and you can usually stop the cause of the cirrhosis of the liver before it progresses further and further.
The key is to get treatment soon enough so that the cirrhosis does not get even worse.