Depends on the conditions, but some reptiles and amphibians do just lay their eggs out in the open, especially if the temperature is favorable. The salamander will likely lay her eggs in a shallow pool and guard them quite closely until the hatch or are removed by staff.
As for lizards, they may have an outside nest, but I wouldn't be at all surprised if they were just laying their eggs inside the house, in an area that isn't frequently disturbed.
Yes, I think I heard about salamanders. Don't they have gills at first when they hatch? Or is that only the newts?
But with the house geckos I find it surprising that its not common knowledge how they lay their eggs. They live close to people for millenia already.
Its hard to imagine how they would lay their eggs inside the house, at least not on the floor. But who knows, appearantly they found a method to survive...