We are travelling from Przemyśl (Poland) to Lviv (Ukraine) next month and when I tried to buy train tickets for the trip using rozklad-pkp.pl I was not able to. However I read on that excellent website maninseat61 that it might be possible to buy them on the Ukrainian Railways site http://booking.uz.gov.ua/en
So I tried and sure enough I was able to buy them. Also bought tickets from Lviv to Kyiv. It was very easy and quick.