According to Wikipedia, the Lake is 17,000 years old, and during the wet season an overflow creek connects it to the Mulgrave River. So it would be easy enough for eels to get into (which can travel over wet ground), and probably any other fish that are in there. Australian fish are great colonists, and even totally isolated waterbodies are often inhabited. If direct dispersal is not possible, they may have arrived via eggs attached to a waterbird or other such random event. Or they might have been stocked by people.
I was told that most of the fish in the lake are introduced Tilapia, but there are apparently several native fish species in the lake too.
the eels are there naturally (as zooboy28 says, the lake connects to a nearby river during the Wet Season). The tilapia seem to have only been there since the 1970s but are well-established. There was a trout hatchery at the lake in the 1930s but that never seems to have resulted in any established trout, and around this time there were introduced "perch" as well which likewise seem to have since disappeared (they were probably some kind of native fish rather than European perch). I can't find anything on any other fish species in the lake.
I was told that there were a few small species of native fish in the lake and they were the same as the fish in other nearby lakes and no one is sure how they got there. Maybe I was misinformed.
Apparently the nearby Lake Eacham has three native fish species - fly-specked hardyhead, mogurnda and Lake Eacham rainbowfish, the latter of which was driven to extinction in the Lake by the illegal introduction of two native species - barred grunter and mouth almighty. The former of those is sometimes referred to as a perch. Other introduced natives in the Atherton Tablelands crater lakes include bony bream, eastern rainbowfish and archerfish.