When installing with APT, it works only with Lua 5.2, and Lua 5.3, but not Lua 5.1 and LuaJIT.
However, when installing with LuaRocks, then it works only with Lua 5.1, and LuaJIT, but not with Lua 5.2, and Lua 5.3.
The error is the same in both cases:

lua5.1: ./curses.lua:1: loop or previous error loading module 'curses'
stack traceback:
	[C]: in function 'require'
	./curses.lua:1: in main chunk
	[C]: in function 'require'
	curses.lua:1: in main chunk
	[C]: ?

This is Debian sid running on amd64 machine.
Note that LuaRocks, Lua 5.1, 5.2, 5.3 and LuaJIT (2.1.0, beta 3) were all installed by APT.