Oh, man, you got caves? Sweet! You could have a great spot for true lagering.
To your question, yes brew a lager style of beer but use an ale yeast. I would explore those caves, safely, and see if you could utilize them for your beer storage. That's what was used before refrigeration.
When I say using the fridge, I mean just use it to condition your beer not lager it. It's really just a spot to keep it cold and give it time to settle out to clear the beer. After it has cleared up some folks transfer to another keg before serving. I skip that and serve from the same keg. You're going to get some cloudiness in first couple pints but no big deal. Dump or drink it, doesn't matter. I drink it.
To your question, yes brew a lager style of beer but use an ale yeast. I would explore those caves, safely, and see if you could utilize them for your beer storage. That's what was used before refrigeration.
When I say using the fridge, I mean just use it to condition your beer not lager it. It's really just a spot to keep it cold and give it time to settle out to clear the beer. After it has cleared up some folks transfer to another keg before serving. I skip that and serve from the same keg. You're going to get some cloudiness in first couple pints but no big deal. Dump or drink it, doesn't matter. I drink it.