How to add shadow to motion graphics lower thirds?

You may not have that ability with a mogrt like this ... this was created in AfterEffects, and the maker only gave you certain options. You can contact the maker, request a change to the mogrt, or you can perhaps change it yourself.

To change ... you would go into AfterEffects, load the mogrt on a "comp" (what an AfterEffects timeline is called), go to the Essential Graphics workspace.

You should see a panel with the settings for the mogrt as shown in your Premiere, and the full things done to it down below to the left of the comp.

You would need to add a drop shadow in those controls by the comp, then drag that up to the EG options box, then save the mogrt. It's not too complicated but might be a bit rough for a first time Ae user.

Jarle's ebook "Making Mogrts" is a downloadable pdf with easy examples to follow, and it would guide you through the whole process ... including creating your own mogrts from scratch. I was the proofreader/grammarian/spellchecker and  a chief tester. It's a great book, all the greater because it's so clear and easy to follow. There's a link to the pdf of the book on this Adobe blog post.

Jarle’s Making Mogrt’s ebook on Adobe blog

Neil

Hi. Make sure to select the text (or another element) in the Essential Graphics panel before applying the Drop Shadow. Also, you can use the Drop Shadow effect.

Just use the Drop Shadow effect in the Effect Controls panel.