Welcome to the forum.
I believe that the paper lanterns are designed for regular copy paper. If you want to try that, the settings are in the material drop down menu under 20# copy paper. When this cuts, the little bits will fly around inside the machine so you have to watch that they don’t block the laser beam and catch fire.
Also, here is a post with lots of information regarding cardstock: Somewhat Comprehensive Testing of Settings for Cutting Paper and Cardstock