Lua - C API - Create variables before running

I would like to extend the Lua so that when a user writes a script, a variable is already available to him.

That is certainly possible. Once the Lua state exists you can create global variables (ie. place key/value pairs in the global environment table).

Is it allowed to create object instances before running a LUA script ?

Yes it is. In my code I preload all sorts of stuff. Tables of useful things for the end-user. Extra libraries they can call.

Example code:

typedef struct { const char* key; int val; } flags_pair;
...
static flags_pair trigger_flags[] =
{
  { "Enabled", 1 },  // enable trigger 
  { "OmitFromLog", 2 },  // omit from log file 
  { "OmitFromOutput", 4 },  // omit trigger from output 
  { "KeepEvaluating", 8 },  // keep evaluating 
  { "IgnoreCase", 16 },  // ignore case when matching 
  { "RegularExpression", 32 },  // trigger uses regular expression 
  { "ExpandVariables", 512 },  // expand variables like @direction 
  { "Replace", 1024 },  // replace existing trigger of same name 
  { "LowercaseWildcard", 2048 },   // wildcards forced to lower-case
  { "Temporary", 16384 },  // temporary - do not save to world file 
  { "OneShot", 32768 },  // if set, trigger only fires once 
  { NULL, 0 }
};
...
static int MakeFlagsTable (lua_State *L, 
                           const char *name,
                           const flags_pair *arr)
{
  const flags_pair *p;
  lua_newtable(L);
  for(p=arr; p->key != NULL; p++) {
    lua_pushstring(L, p->key);
    lua_pushnumber(L, p->val);
    lua_rawset(L, -3);
  }
  lua_setglobal (L, name);
  return 1;
}
...
  MakeFlagsTable (L, "trigger_flag", trigger_flags)