There are no other direct flights from the UK. Any connecting services are (as you've found) likely to be very expensive.
Source:
http://en.wikipedia.org/wiki/Lviv_Internationa l_Airport
(I was forced to refer to Wikipedia because the Lviv Airport website is only available in Russian).
The best solution is probably to fly, with Ryanair, from Luton to Rzesz�w (which is just over the border from Lviv, in Poland).
http://www.ryanair.com/site/EN/
Then take the shuttle bus to the rail station:
http://www.lotnisko-rzeszow.pl/katalog/dojazd/ en/rz_dojazd.php
From there, the Thomas Cook Rail Map of Europe shows a direct line to Lviv. I've been struggling to find any useful information on the websites of either the Polish or Ukrainian Railways. (I also can't get the German Rail website, which covers the whole of Europe, to recognise 'Lviv' as a destination).
However you should be able to get the relevant information by phoning Deutsche Bahn UK, on 08718 80 80 66 (8p per minute, 0900-200 Mon-Fri. 0900-1300 Sat &Sun) or you can email them:
[email protected]
Alternatively, Rail Europe might be able to assist:
http://www.raileurope.co.uk/Default.aspx?tabid =508
Chris