Can you mix lager and stout?

Yes, it is typically called a "black and tan". If done properly, the lager will clearly settle on the bottom, and the stout should remain on top.

That is not correct....

A lager and a stout like Guinness (Stout) and Harp (lager) is called a half and half

A Stout and a pale ale or ale is a black and tan. Most people use Guinness for the stout and bass for the ale.

You can use any Stout and any lager to make a half and half

and you can use any stout and any ale to make a black and tan...