Interesting question....in my case, being alone, and loneliness were not the same. I've been to group functions, (mostly before recovery), surrounded by people, and felt lonely as hell.
In recovery I've gone thru periods of isolation; meaning, I go to meetings, and thats it. No other contact with meeting people. So I was alone. Sometimes I was fine with it, sometimes I felt lonely.
The way I'm learning, to alleviate the loneliness, is by making a connection with somebody, somehow. Though the internet by itself does not do it for me. It helps while I'm online, but fades away as soon as the computer shuts down. Actually personal connections can be felt much longer, in my experience, can last the whole day.
For some, myself included, it can be a very big wall to climb.