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they talk about replacing it in the appendix if it you don't want to use extra libraries https://buildyourownlisp.com/appendix_a_hand_rolled_parser#replacing_mpc Alternatively you could read through the library source code and make your own implementation, it's a single source file and it's quite legible https://github.com/orangeduck/mpc/blob/master/mpc.c
If you learn well by looking at code then check out some small projects. Lua is possibly a little too much at this point. Perhaps PicoC?
Since no one has said yet, how about write-a-C-interpreter? is a tutorial on how to write a C interpreter in C, you might want to take a look.