Your dungeon is a salt mine.
I knew about the salt mines under the Great Lakes but did not realize that many other huge salt mines are also beneath bodies of freshwater.
As is evident from the details provided, the majority of these
underground mines are enormous in size, occupying multiple square
miles far beneath the Earth’s surface. It is also fascinating to note
that many, if not most of these mines, extend beneath a large body of
water (many of which are freshwater).
I wondered why the lake did not just drain into the mine. Exactly that happened to one of these salt mines under a lake in Louisiana. Interesting reading! https://en.wikipedia.org/wiki/Lake_Peigneur
Your dungeon is deep and protected from surface water by an impermeable stratum. Maybe it actually is a salt mine. Salt is easy to dig and carve, omce you get down to it. The overlying lake will come and go with the eons and currently the area is filling back up, so the region over the mine / dungeon has become wetlands. Deep below, the mine / dungeon stays dry.
A salt cave as a dungeon offers opportunities. Here is an image of the Wieliczka salt mine, which contains a cathedral carved entirely from the salt. With a name like yours, maybe you have been there?