Well about 40km around there are few mines, so maybe that etymology is correct.

"A different interpretation is suggested by the Hungarian name "Lukácsbanya", i.e. "Luke's Mine", which is also the meaning of Slovak Banja Luka."

.. just wanted to say else that Luka does not mean any name Luke nor Lukáč in Slovak, but it's a meadow just like in your language. So there are mines under meadows? That sounds more logical than a mine of some unknown Lucas.