Yes, downloading the web page is the easiest part of all, for example you can use Notepad, Textpad or Notepad++ to open the URL, and write some sort of regex macro script to extract the special lyrics text string, which needs to be HTML decoded to become a unicode string.
On the commandline WGET and FINDSTR should also do the download and extraction job.
For the HTML decoding part I did not find a commandline tool yet, which supports decoding from ascii file to unicode file, giving the proper unicode characters.
The main problem is the integration into Mp3tag environment.
(Note: Hereby I claim the rights of naming the process "lyripping" and the tool "Lyripper")
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How can Mp3tag provide the URLs to the lyripping tool?
-- Many URLs by one export script?
-- One URL for calling directly a defined tool from the track's context menu?
(... this would be a worse solution because Mp3tag does not support "RunWait" per track file).
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How will the resulting text file be saved into a tag-field per track?
(... sure by action import textfile).
So far for now, I have already a working prototype script, written in the WinBatch Scripting Language. But I will check other options too.
Once you have the html text file at your desktop, name it properly to link it to the related track, then the text can be loaded into a tag-field and can be manipulated using regular expression down to the needed lyrics text. Even the HTML decoding could be realized using the Mp3tag Scripting Language, anyway, in endless scripting expressions, maybe not perfect at all but with some useful result.
Note:
If the Mp3tag websource application programming interface would be open source, then such a simple requirement for fetching some text from somewhere from the net and writing it directly into a tag-field, this workflow would be rather easy job.
I am sure, that many people would have fun to create those helpful "Mp3tag-Apps".
DD.20110610.1306.CEST
Is that the quality standard for the texts in metro lyrics? 
That is:
"I want to thank you falettinme be mice elf agin"
Should be:
Thank You For Letting Me Be Myself Again
DD.20110610.1523.CEST