Recommended reading order:

lmathlib.c, lstrlib.c: get familiar with the external C API. Don’t bother with the pattern matcher though. Just the easy functions.
lapi.c: Check how the API is implemented internally. Only skim this to get a feeling for the code. Cross-reference to lua.h and luaconf.h as needed.
lobject.h: tagged values and object representation. skim through this first. you’ll want to keep a window with this file open all the time.
lstate.h: state objects. ditto.
lopcodes.h: bytecode instruction format and opcode definitions. easy.
lvm.c: scroll down to luaV_execute, the main interpreter loop. see how all of the instructions are implemented. skip the details for now. reread later.
ldo.c: calls, stacks, exceptions, coroutines. tough read.
lstring.c: string interning. cute, huh?
ltable.c: hash tables and arrays. tricky code.
ltm.c: metamethod handling, reread all of lvm.c now.
You may want to reread lapi.c now.
ldebug.c: surprise waiting for you. abstract interpretation is used to find object names for tracebacks. does bytecode verification, too.
lparser.c, lcode.c: recursive descent parser, targetting a register-based VM. start from chunk() and work your way through. read the expression parser and the code generator parts last.
lgc.c: incremental garbage collector. take your time.
Read all the other files as you see references to them. Don’t let your stack get too deep though.