What do you think of when you think of lonelyness?
What sounds do you hear when you are alone?
Make a list, those are all things the camera can look at and the audience can hear. We've all been lonely, it's not a unique thing, so if you can show things that make you feel/think lonely, it's most likely that other people will react similarly.
As for the fact that you might want to just add an interesting element, you could film someone watching who is also alone, so really, in the end, they aren't alone at all, just one of them doesn't know it.