(2-part post):
Unfortunately, the Lvov Airport website is 'under construction'. That makes researching suitable flights much harder than it should be. However, Wikipedia provides some clues as to possible routes:
http://en.wikipedia.org/wiki/Lviv_Internationa l_Airport
Ukraine International will fly you to Kiev (for an onbound connection to Lvov) from Gatwick.
Taking Mushroom25's reference point of random dates in August, the international fare (return, inc taxes & charges) is �270.64.
For the domestic flight to Lvov (return, inc taxes & charges), the fare quoted is US$160.36, bringing the total to roughly �350.
Ukraine International's daily flights tie up quite well outbound:
Depart Gatwick 11130, Arrive Kiev 1650
Depart Kiev 1920, Arrive Lvov 2030.
However, the connection is probably too tight on the return journey, so you might need to stay in Kiev for a day:
Depart Lvov 0700, Arrive Kiev 0805
Depart Kiev 0900, Arrive Gatwick 1030
http://www.ukraine-international.com/eng/uk.ht ml