If you are planning not to waste your time while going to Lviv, the most easiest and convenient way is to take a plane from your native town and flew to Poland. If your airplane is landing at Rzeszow, you can take a bus to Perzemysl and from here to use the services of express buses going to Lviv. It takes only 4 hours to get to Lviv by them and the detailed timetable of such buses you can find here:
http://www.pks-przemysl.pl/index.php?url=strony/lwow
Have a nice trip!
Oksana