Cy-gone... yes, no rescue mission needed!

Re Diners... there's two lounges in Lima, both in the International Terminal One is outside of customs but the other is in the duty-free area (look for a staircase, I believe it is signed) so I think you can get to it while in transit. Guests are OK. For details, see
http://www.dinersclub.com/lounges/peru_2.html