You could create a nomenclature. To add a symbol to the nomenclature, go to Insert --> Nomenclature entry, or click the toolbar button:
In the window that appears, type the symbol as LaTeX code, e.g. $\mathbb{R}$, in the Symbol field.
To create the sorted list of all the entries you have created, choose Insert --> List/TOC --> Nomenclature.
To change the name from Nomenclature to e.g. Symbolverzeichnis, add to the preamble
\renewcommand{\nomname}{Symbolverzeichnis}
The preamble is found under Document --> Settings --> LaTeX preamble.
Increasing space between symbol and description
Right click the Nomenclature heading in LyX (what gets inserted from Insert --> List/TOC --> Nomenclature) and choose settings. Set the List Indentation to Custom, and put in the length of your choice. (5 cm, as in the below screenshot, is probably a little too much ...)

One note
When testing with the absolute value, $|x|$ I couldn't get that to work (no idea why). As a workaround I used \lvert and \rvert from amsmath instead. If you haven't used any other math constructs that requires amsmath, you may have activate that package manually, which you can do under Document --> Setting --> Math options. Uncheck "Use AMS math package automatically", check "Use AMS math package".
