Hi! Welcome to pet talk! I hope you enjoy it here. ^_^

Have you ever taken your Lhasa to obedience classes? They might help with him - but make sure you find a class that uses positive reinforcement (like clicker training), because if he can be agressive you don't want to use any harsh training methods.

As for your Eskie, you're not alone - it's a natural doggie trait! But I can understand that you wouldn't want big holes in your yard.

Do you keep her outside alone when she digs, or is she with you? She may be digging out of boredom. Do some activities with your pup, like play fetch, or take a long walk. That will tire her out, and she won't dig out of boredom. Also don't leave her outside alone.

Is she digging along a fence? In that case, she's trying to escape. This is probably out of boredom too - so exercise her, but also you should reinforce the fence with cement or something so she can't dig under it - because you don't want your pup to escape from the yard.

And if after all that she still digs, then you should give her a place of her own to dig, like a sandbox or a special patch of dirt. Show her that it's okay to dig there, by burying biscuits and letting her dig them up, and praising her for digging there. And put a little fence around gardens - since dogs love to dig in soft soil. Make sure she knows not to cross the fence.

Good luck!!! I hope that helps!