It seems to be necessary to select the file, select tag source, confirm URL, confirm tag fields to be imported and this one by one for each desired file. I usually confirm everything and do not modify settings there. So I have to repeat these steps many times.
As I have already automated a lot using action groups which are applied to a bunch of files I'd like to add one more action which imports the lyrics operating the above mention steps automatically for all selected files.
Several "no"s at this point:
No, it is not possible to get data with web source scripts for several files that do not belong to 1 album.
No, it is not possible to get the lyrics for several files unless they feature the same lyrics.
No, it is not possible to call a web source script with an action.
In respect to searching the lyrics: there are several plugins for Foobar2000 that look for lyrics in various sources and in sequence for all the selected files.