As I can see in the Polish part of the Internet - there is no direct bus connection from Zamość to Lwów. The buses from Warsaw and Lublin to Lwów go through Zamość, but they have no stop there. So, going in an opposite direction you may try asking the driver of such a bus if you could leave in Zamość, but in a journey to Lwów it's practically no way to make use of them.
Another option is to get from Zamość to Tomaszów Lubelski and from there to Lwów. There is no problem with the first part, there is plenty of buses on this route. But there may be problems with connection from Tomaszów to Lwów.
Here: they write that a bus from Tomaszów to Lwów goes from Tomaszów at 6:35 a.m. 11:00 a.m. and 1:40 p.m., but I don't know if this info is still valid (this news is from a year before now) - and it is not clear, it might be understood also as 11 a.m. and 1.40 p.m. are departures from Lublin. You may try to call the bus terminal in Tomaszów - 502-371-407 - but I am not sure if they speak English. And it's never certain that the bus to Lwów will go, it must return from Lwów first.
They return bus Lublin - Lviv . Since January abolished exchange carriers were Polish and Ukrainian . Companies do not have the required permits .
After completing the formalities have already returned connection Lublin - Lviv Nikolaev by . Bus leaves from Lublin after 16.00 .
From Saturday to Lviv will be able to go from Tomaszow Lubelski , departure at 6.35 .
Probably the weekend will also ride buses from Lublin to Lviv at 11.00 and 13.40 - Zdzislaw Stelmach announces Tomaszów bus - u.
With bus connections between Lublin and Lviv are mainly used by Ukrainian and Polish students . Since January the only direct connection was through bus from Lodz, Lublin, which was before midnight.
Quite a popular option to get to Lwów from Poland is through Przemyśl, but from Zamość it's a very round way.
From Przemyśl to Lwów there are a few options:
- by train - rarely, expensive (international prices), and long time because the train have to change wheels (in Ukraine they have different track gauge)
- by direct bus - here are some timetables: pks-przemysl.pl/rozklad-jazdy-miedzynarodowy.html - two different on a website of the same company, so I have no idea which one is valid (however, I know that they also sometimes do not go because the bus haven't returned from Lwów yet), but it seems to be the most reasonable way
- by a local bus to the border crossing, then cross the border on foot and catch a Ukrainian local bus to Lwów - they go quite often so it seems to be the most reliable, and the fastest because you don't wait so long on the border crossing
Connections from Zamość to Przemyśl you may find at e-podroznik.pl. Some of them are with a change in Jarosław, maybe there are some connections to Lwów from there...
I have also read about some buses from Tomaszów Lubelski to Rawa Ruska, which are used mainly by smugglers (which go officialy from the coach terminal in Tomaszów, but they are not easy to find them there) - but it was forum posts from 2009 - so this info might be outdated. However, from Rawa Ruska there is plenty of buses to Lwów.