Yeah, as I said I'm not sure but I don't intend to make many lagers. I could always lager in kegs in another chamber/freezer.
I would be happy if I can keep the beer at ~60. I have had success lagering in a similarly sized chamber with a similar A/C unit. The design of that one made it much easier to keep in cold air, it was just a pain to get into (open top). I am optimistic that if I seal it well it will do what I need.
I have a bigger A/C unit (12k BTU) sitting around but I was hoping to sell it. It is huge, heavy and power hungry but I guess I could use it.
EDIT: On Saturday I will turn it on and sit inside to simulate the heat of fermenting beer
and I will let you know how cold it gets.