Can ghosts be killed?

Ghosts can be killed, but it requires an environmental object that's not present in The Lich Yard; so no, you can't kill the ghosts in that level.

There's an optional zone later on that has the necessary objects laying around, and in fact the goal of the level is to do a bit of ghost busting.

This is a bit spoilery if you haven't made it to that level, so I've hidden it below:

In the Hall of Heroes, accessible partway after defeating the second map, you'll find some mysterious light orbs:

Smack these orbs with your shovel to make them leap up and explode:

This lightsplosion will destroy any lingering ghosts; once all ghosts in a room are dealt with, the lights will come on (as seen in the background of these images).