I think it depends on your personality, lifestyle and reason for living in Ukraine. But, there are some common factors which will influence loneliness.
The cost of communication can have an effect when living in Ukraine. Not all friends and family have Skype, WhatsApp of Facetime and still rely on phone calls to talk. Phone calls can become quite expensive when calling abroad and some friends don't want to call because it will cost them money.
For me, I like the solitude that being an expat brings. I enjoy time by myself, so it isn't a problem when I find that I am at home alone.
On the other side, marrying someone who already lives in Ukraine means that you meet new people and make new friends. My fiance introduced me to many new people and some of those have become good friends now. I think it is possibly more difficult if you are single in Ukraine.
I would also recommend learning either Ukrainian or Russian. Not being able to speak their language is very isolating. Most people that I meet do not speak English, so I need to be able to speak either Ukrainian or Russian. I practice and learn everyday, and everyday it gets a little bit easier.
I hope that helps...