I hope this will be helpful for anyone who wants to travel from Rzeszow to Lviv. I travelled from Rzeszow to Lviv on the non-stop overnight sleeper train mid-November and it was great! I purchased the return tickets in advance from excitingpoland.com who were extremely helpful. I flew from East Midlands airport to Rzeszow by Ryanair, then got the "L" bus to Rzeszow centre costing 8pln each way. The train station is across the road from where the bus stops. The bus station is also across the road so you could get the bus too. I asked about prices and was told 37pln each way to Lviv. The train station in Rzeszow is very clean and there is a bar area that sells hot and cold drinks and snacks. The ticket offices at the train station in Rzeszow are open until well after midnight so you could buy your tickets on arrival at the station.
There wasn't a direct train back from Lviv to Rzeszow to get me to the airport in time for my flight back home but I understand that there are some direct trains. However, the train left Lviv station at 7.19am and arrived at Przysml at 9.55am. You need to allow plenty of time for your connecting train to Rzeszow because of the time spent on the borders. It took 1.30mins for the train I was on to get through the border controls but that's because the guards found someone carrying something they shouldn't have. I then took the connecting train from Rzeszow leaving at 10.40am and arrived at Rzeszow at about 11.45am. You need to be aware that the bus from Rzeszow centre to the airport leaves at 12.25pm and the next one isn't until 16.40pm and takes 25 mins. I took a taxi from the train station and it cost 50pln.
I have travelled by car from Rzeszow to Lviv before and found the queques on the borders to be horrendous. I must say that this is definitely a much easier, less stressful option. And I would highly recommend using excitingpoland.com to book your train tickets in advance.