The blue-tongue lizards have a very catholic diet eating soft plant matter, flowers and fruit, crunchy beetles and other insects, spiders, small lizards, even silly young birds who venture too close, in fact they will eat almost anything that is slow enough and will fit into its large mouth, this also includes garden snails which they are able to crush with their strong jaws, so placing fingers near their mouth is not a good idea. Their limitation regarding diet is governed by their small legs and large body, which apart from a short lunge, mean they are normally quite slow and usually only able to catch slower prey.
As a word of caution, if you are fortunate to have these skinks living in your garden, please do not use snail pellets as they will eat the dying slugs and snails and become poisoned themselves. Best to leave it to your blue-tongue lizards to control your slug/snail problem.
Western Blue-tongued Lizard, Tiliqua occipitalis
Blue-tongue lizards are quite common in most capital cities these days, possibly as there are fewer predators who wish to eat them, rather, most domestic animals are more curious and easily discouraged by their aggressive display. To attract them to your garden, place large logs, rocks and have plenty of ground cover in which they can shelter. Do not use snail pellets and watch out when mowing. Then besides a harmless, attractive, interesting and interactive garden resident, you also get a free creepy crawly and expert snail catcher to boot. Sounds like a good deal to me!