Not only does Lotor take the exact same forms of his father’s, with the handle having the same shape, but Zarkon has also shown no surprise that Lotor can use it. Heck, the fact that Lotor even can use it. 

There’s also the sadness on Lotor’s face. This is something dear to him, which he will now use to fight the man who taught it to him. 

We are not done seeing flashbacks of the Galra royal family. I have an inkling that we might see an image of Zarkon teaching Lotor how to use it before Lotor was assigned the planet he mentioned.