cd into the desktop and try a new folder from there?
I did;
cd desktop
mkdir test
A new folder called test popped up. Suggests to me that it might be your syntax?
EDIT:
Whilst testing I found the same as you if you are not CD'd into the desktop. What I didn't notice straight away is that the folders were actually being produced but at the top level of the users folder. Don't know why though.
So, the cd desktop command followed by the mkdir test command gave me a new folder on the desktop.
But typing mkdir /Users/JohnDoe/Desktop test gave me a folder at the top level of my users folder.
2nd EDIT, try the following;
cd desktop && mkdir test or in your case cd desktop && mkdir -p lizz01