Is it possible to visit Lake Hillier?
Do I have to go with tour or can I for example rent a car and go there? I see no roads near it.
I would try contacting Esperance Tourism, and asking them the best way to see this specific island (Middle Island, in the Archipelago of the Recherche).
It's on an island off the coast so driving is not an option. I would imagine there would be a ferry, as (from the link) they are promoting the Archipelago as a tourist destination.
Esperance is a long way from both Perth and Adelaide (the two closest capitals), so I would recommend you line up some other things to do down there too.