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This was a list I got in my mind without googling... for more inspiration and see what others are doing take a look at awesome Lua: https://github.com/LewisJEllis/awesome-lua
check out https://astronvim.github.io/ - a NeoVim IDE & help enhance it with repl features https://github.com/AstroNvim/AstroNvim/issues/1553
create a lua shell the way xonsh is a python-powered shell
create a repl to the standard that ptpython sets for python (both croissant and ilua leave a lot to be desired)
To answer the OP's question, you could tackle luv and libuv ecosystem, as a way to connect Lua to real-world systems (files, sockets, servers...). That's one way to put Lua skills to use, there are other great answers in the thread. Another recommendation is to go through Programming in Lua book, especially the later chapters where you learn how Lua talks to the host application.