> Can someone indicate how to typeset
> $L_{α+β}$
> as verbatim text?
> (\arg{} doesn't help here...)

Untested:

\type{...} should work. (Definitely did work a couple of months ago).

> Furthermore, I suppose that typesetting Greek characters verbatim
> depends also upon which \tt font is being used.

CM Unicode has a good coverage of greek characters in typewriter font.

Aditya