Don't despair, Weecalf! Chambers Dictionary is almost an essential for such crosswords. Click
http://www.chambersha...s/chref/chref.py/main here and the link will take you to an appropriate website.
Type the word be into the top slot, ensure the next slot reads Chambers Thesaurus and click on submit. On the first line it offers, you'll see the word 'lie' which explains the 'eil' part of Eileen as outlined above.
You can, of course, change the Thesaurus slot to make it the Dictionary slot or vice versa by clicking on the down arrow.
Stick with it!