I've done both. Let me tell you, embedding Lua into a C program is magnitudes easier than embedding Python.

The main reason is the endless fragility of Python's garbage collector. To be clear, the API is trying to be as helpful as possible, but it's still a whole bunch of complexity that's easy to mess up. Incidentally, this discussion is left out in the linked article, which makes it less than useless. In my experience with many a third party C/Py interface, data leaks are incredibly common in such code.

Lua of course also has a garbage collector, but it essentially only knows two types of values: POD, and tables, with only the latter needing much consideration. The interaction model is based on a stack-based virtual machine, which is more complex than Python's full-function abstraction, but conveniently hides most of the garbage collector complexity. So long as you're just reshuffling things on the stack (i.e. most of the time), you don't need to worry about the garbage collector at all.