Exceptions in Lua are emulated with LUAI_THROW, LUAI_TRY, and luai_jmpbuf.

Interestingly, if you compile Lua with a C++ compiler, standard C++ exceptions will be used. If a C compiler is used, they will be emulated with setjmp and longjmp.

/*
** LUAI_THROW/LUAI_TRY define how Lua does exception handling. By
** default, Lua handles errors with exceptions when compiling as
** C++ code, with _longjmp/_setjmp when asked to use them, and with
** longjmp/setjmp otherwise.
*/
#if !defined(LUAI_THROW)				/* { */

#if defined(__cplusplus) && !defined(LUA_USE_LONGJMP)	/* { */

/* C++ exceptions */
#define LUAI_THROW(L,c)		throw(c)
#define LUAI_TRY(L,c,a) \
    try { a } catch(...) { if ((c)->status == 0) (c)->status = -1; }
#define luai_jmpbuf		int  /* dummy variable */

#elif defined(LUA_USE_POSIX)				/* }{ */

/* in POSIX, try _longjmp/_setjmp (more efficient) */
#define LUAI_THROW(L,c)		_longjmp((c)->b, 1)
#define LUAI_TRY(L,c,a)		if (_setjmp((c)->b) == 0) { a }
#define luai_jmpbuf		jmp_buf

#else							/* }{ */

/* ISO C handling with long jumps */
#define LUAI_THROW(L,c)		longjmp((c)->b, 1)
#define LUAI_TRY(L,c,a)		if (setjmp((c)->b) == 0) { a }
#define luai_jmpbuf		jmp_buf

#endif							/* } */

#endif							/* } */

An errorjmp is defined in Lua state. It's a linked-list for recording a series of jump location of the current error.

/* chain list of long jump buffers */
struct lua_longjmp {
  struct lua_longjmp *previous;
  luai_jmpbuf b;
  volatile int status;  /* error code */
};

// error codes
/* thread status */
#define LUA_OK		0
#define LUA_YIELD	1
#define LUA_ERRRUN	2
#define LUA_ERRSYNTAX	3
#define LUA_ERRMEM	4
#define LUA_ERRGCMM	5
#define LUA_ERRERR	6

lua_longjmp is used in the luaD_rawrunprotected:

int luaD_rawrunprotected (lua_State *L, Pfunc f, void *ud) {
  unsigned short oldnCcalls = L->nCcalls;
  struct lua_longjmp lj;
  lj.status = LUA_OK;
  lj.previous = L->errorJmp;  /* chain new error handler */
  L->errorJmp = &lj;
  LUAI_TRY(L, &lj,
    (*f)(L, ud);
  );
  L->errorJmp = lj.previous;  /* restore old error handler */
  L->nCcalls = oldnCcalls;
  return lj.status;
}

luaD_rawrunprotected is used in the luaD_pcall.

int luaD_pcall (lua_State *L, Pfunc func, void *u,
                ptrdiff_t old_top, ptrdiff_t ef) {
  int status;
  CallInfo *old_ci = L->ci;
  lu_byte old_allowhooks = L->allowhook;
  unsigned short old_nny = L->nny;
  ptrdiff_t old_errfunc = L->errfunc;
  L->errfunc = ef;
  status = luaD_rawrunprotected(L, func, u);
  if (status != LUA_OK) {  /* an error occurred? */
    StkId oldtop = restorestack(L, old_top);
    luaF_close(L, oldtop);  /* close possible pending closures */
    seterrorobj(L, status, oldtop);
    L->ci = old_ci;
    L->allowhook = old_allowhooks;
    L->nny = old_nny;
    luaD_shrinkstack(L);
  }
  L->errfunc = old_errfunc;
  return status;
}