I don't agree that Lima is particularly dangerous these days, although I'm sure there are parts that are. I spent a week there last year and it felt a lot safer than it was in the late 80's. I had no problems walking through the centre in the late night.
The Diners Club lounge is pretty good and there is one either side of immigration. I think non-cardholders can pay to use it and as well as snacks and soft drinks, they provide free Pisco.
There is a luggage deposit at the airport for a couple of dollars.
If you don't have any plans on how to spend the day, I'd catch a taxi to the Gold Museum and then cross the main road (I think on the next block across from the museum) and there is an excellent seafood restaurant where you can have great ceviche along with a couple of Cusquena beers. Then you can get a cab into the centre for a bit of a wander around the beautiful plazas for the evening before heading back to the airport.
Enjoy the day