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In fact it is not as difficult as you might think. You need to load the "Customisable lists (enumitem)"-Module via Document -> Settings -> Modules -> List Enhancements.
Then you can put this in your Preamble:
\setenumerate{label=exercise \arabic*} (Mention, that LyX gives you an error, if you're ...

Thanks for the Welcome

Just in case someone else struggles with the same problem.

It was just a case of rtfm:
You have to go on edit -> custom text styles -> choose the thing you need

After this you can use the insert-menu...

I'm using LyX-version 2.4.1 under Windows 11

I try to make my first presentation with LyX using the beamer-presentation-class.
I'm trying to use overlays within a line, but the method shown in the LyX-Beamer-manual is not working, because there is no "Overlay Specifications" or "Action ...