What I’d be inclined to do is forget the Corona bit.
Raycasting is raycasting. There are plenty of tutorials out there (I found this one) http://lodev.org/cgtutor/raycasting.html - or this one http://www.permadi.com/tutorial/raycast/rayc7.html - find one you like and work through it, but write it in lua rather than C or C++ or whatever. It shouldn’t take very long to work through.
You will get a much better choice of algorithm if you look at all the raycasting/faux 3D tutorials rather than those specifically for Corona. (Not knocking corona at all here).
Most of those work on ray projection and rendering a strip scaled appropriately. It should be possible to optimise it for 2.5D by say looking for boundaries - where the ray ends up on a different plane, so rather than doing ray trace/draw ray trace/draw you trace the rays and figure out a quadrilateral and draw that - there almost certainly will be some work in this sort of thing. Most of the original raytracing code is from DOS days where you would literally write to pixel memory, a different approach would be needed for using modern graphics cards. In the picture of the Corona one, if it is ‘classical’ there will be a lot of strips of textures, left to right, whereas in Corona you can probably draw it with about half a dozen 2.5D Polygons.
This one looks quite interesting http://www.permadi.com/tutorial/raycast/ - it starts with the basic “Wolfenstein” design - everything square and flat and develops it. But pick whichever one you like. It would probably cover most of your list.
There are other alternatives ; you could adopt the ‘single room’ approach used in Paul Woakes’ Mercenary games for example. It really depends what you want to do.
