What is killing the branches on one of my Lilly Pilly Plants?

Thank you for contacting Yates. 

We would suggest have a close check and see if the tree is affected by borers. 

Unfortunately, as yet we don't have a product that is registered to treat borers in trees. To reduce and prevent borer infestation, we recommend improving the health of the plant and try to prune the stems/branches that are infested where possible. You could also make a lance out of a metal coat hanger and lance the borers down the hole/s, however, this is a rather crude form of control. Arborists may also be able to further assist you with advanced trees as they may have access to products for chemical control.