Cara
About the best I can suggest is repotting them into some fresh mix.

If you get rain in autumn, now would be a good time to do this.

I bought a Syzygium last year and repotted promptly as it was very pot-bound. I used a bonsai-type mix- very free-draining with 5mm grit, but with some added humus as I know they like a rich soil that holds moisture. If your mix has been drying out too quickly because the roots have filled the pot, or it lacks humus, then your plants won't be able to repel 'invaders'.

Don't take too much of the root ball back. Leave about a third and take out the older brown roots, leaving the young white growing tips as much as possible.

When you've done it, put it on either the south or east side of the house and keep it just moist for about a month. Dunk it about once a week, wait until the bubbles stop, and let it drain, not stand in water.

After the first month has passed from when you repotted, you might want to give it a monthly liquid fertiliser feed. Miracle Gro has been pretty good for my plants.

If they make growth over winter, check again in spring to see if the roots have colonised the pot. If they have, and you've got good top growth, too, pot on without disturbing either top or roots.

If it's really booming - do another check next autumn. I've got a Coprosma that's only about 15cm high but grows furiously so it needs repotting twice a year. I'm not sure how fast your lilly pillies will grow, but keeping an eye on root growth is a prudent thing to do to keep pests away. And thorough watering.