Lima airport tax. If you leave the airport to stay in Lima you will need to go through passport control. I was told that once you have your passport stamped, then you must pay the $25 departure tax when you get your boarding pass for the next international flight. The entry way to the boarding gates has an electronic device which reads your tax stamp so you can't get back to the international departure gates without the $25 tax stamp.
When you get your boarding pass for Cusco you must pay a $4 tax before you can proceed to the gate area. In Cusco you have to pay $4 to go back to Lima.
In Quito, after you have your boarding pass, and if you are leaving the same day you arrived, you can get a tax waiver for in-transit passengers. I stayed in a hotel for the day and did not have any problem getting the transit waiver because I flew out on the same date.