When some people use the word "lonely," they often mean something fairly different from my definition of the word. Often when people say that they are lonely they mean simply that they aren't having sex as often as they would prefer. That's, I suppose, one definition.
At first I thought there were only two definitions—actual loneliness, and turgidity-of-reproductive-organ loneliness—but now I think that there are at least three. I think that some people are lonely like they're lonely for a million dollars. I would like a million dollars, but I have no valid reason to expect a million dollars, so it causes me no real pain that I don't have a million dollars. I think that's the key. Ideally, I can see the value in having a companion. (I can also see the personality nuances that could make the endeavor fairly challenging.) However, it brings me no pain to know that I do not have such a companion. Therefore, by my definition, I am not lonely. (I'm purposely ignoring the fact that loneliness can also easily deal with being around multiple people, and doesn't have to be specific to a single companion.)
When I say I live alone, occasionally people will ask if I'm lonely, or just assume that I am. But I'm not. I don't yearn for someone; I simply don't have someone. The fact that I do not have someone doesn't make me depressed. I merely recognize that, at some point, I could be potentially happier with a mate. I could be happier with a million dollars also. Or, possibly some combination of the two.
Some people call that loneliness, and I think it's incorrect. Perhaps people who are themselves lonely, and assume that all other single people are too.