I don't speak or read Ukrainian and couldn't make much sense of the Ukrainian rail system's online info (which I'm told wasn't accurate in any case), but I wanted to get back and forth to Lviv (from Krakow) and my window of opportunity was limited. It seemed that the number of trains and seats was also limited, so I really wanted to nail down the tickets and reservations in advance.
I tried working through RailEurope, but despite valiant attempts they weren't able to get it done. Similarly, I wasn't able to meet the goal via email correspondences with the concierges at my hotel.
Finally I hit on Polrail.com - hurray! Not only did they (Daniel and Jeff both helped) work with me in English online, but they were able to arrange to have all the required tickets and reservations waiting for me when I reached Krakow (and gave me English language confirmations!).