When the master lich levels up and becomes an Arch-lich, will it die if they have been genocided

As far as I know, there's no way to train or otherwise cause your pet to be more aggressive. In general, pets don't much care if a monster is friendly to you or not - they'll go ahead and attack anyway, as long as the monster is close to their level.

It's quite possible that your dog has reached max level by this point in the game, especially if he's been getting a lot of kills. However, dogs don't normally attack shopkeepers, even at max level.

I can think of a couple possible explanations for your situation:

• You're wearing a ring of conflict. (Unlikely, since you'd be getting attacked too.)
• Your pet was at maximum level and ate a wraith corpse. This would put him within a level of the shopkeepers and liable to attack.

Some pertinent info from the wiki article on pets:

They say discretion is the better part of valor. Pets don't always possess such discretion, and often find themselves overpowered by opponents they take on. Although a pet will not attack a monster which could kill it in one round, this calculation takes no account of the monster's weapon or passive attack. Be especially careful about bringing dogs or cats into the Gnomish Mines, or horses into shops, especially in the deeper levels. Horses seem especially vulnerable to mimics, and have also been known to attack shopkeepers, as they reach a higher level than dogs or cats. (A pet will not attack a monster which is two or more levels higher than itself. A fully grown large cat or dog is level 9, a fully grown warhorse is level 10, and a shopkeeper is level 11.)

also

Carnivorous and omnivorous pets will eat wraith corpses and gain one level for each, capped at 15 over base level. (There is no cap for gains from engulfing live wraiths.)

Ranged attacks, with the exception of force bolt/wand of striking (which destroy the boulder in the process), pass over boulders just fine and let you kill whatever is on the other side.

If you don't have any ranged weapons or suitable attack wands of spells, in the worst case you can leave sokoban, smash a boulder, and get rocks to throw.

If you have a wand of teleportation, you can also teleport the boulder (and, in the long hallway, probably the monster behind it as well) with no luck penalty. Note that the boulder way very well end up in an inconvenient place.