Will a pet arch lich still be covetous?

My pet dog got polymorphed into a demilich, and has since grown into an arch lich (L37 HP291 AC-21 invisible fast). This is great for now, because I've yet to find Medusa, and the extra firepower is very useful. However, I'm concerned that it will grow too powerful to defend against should it turn on me. It's already more than double my HP and very close to matching my AC. I keep a few genocide scrolls handy, just in case, as well as minding that I stay on same level to prevent it going feral. I've read that arch liches covet the book of the dead. Will I have a problem should I get as far as retrieving the book, and performing the invocation ritual?
PS I'm a human healer, and trying the "protection racket" for HP boost, so my XP is still quite low as I'm making my way to the Valley now. By then, I may have an extremely high AC and a generous HP. But, at the rate the lich is getting stronger, I'm afraid it may become a serious threat should it turn on me.

Looking through the source for monster movement yields this:

/* my dog gets special treatment */
if (mtmp->mtame) {
    mmoved = dog_move(mtmp, after);
    goto postmov;
}

...

/* and the acquisitive monsters get special treatment */
if (is_covetous(ptr)) {
  ...

In other words, movement for tamed monsters is handled before the covetous check, meaning that as long as the arch-lich stays tame it shouldn't bother you.