Something to add about the adjective 'lone': Unusually, 'lone' is an adjective which is always found in combination with a noun, almost as a set phrase, such as lone wolf, lone star, lone ranger, lone parent, lone survivor. In the past, 'lone' could be used like any other adjective, but now it appears only in certain collocations. Lonely, by contrast, is an adjective that can be used freely in any grammatical context.

"lone wolf" is a term used to describe a person, but if it were actually describing a wolf: "a lone wolf" means the wolf is alone "a lonely wolf" means the wolf is alone and feels sad about it.

I would say that 'lonely' is a temporary adjective. You could be lonely or feel lonely one day but the next you may no longer be lonely. 'Lone' is more permanent. A 'lone wolf' is an expression used to describe somebody who prefers or has a tendency to be alone (by themselves). Lonely is more commonly used. Hope that helps!

The meanings overlap, but usually: "Lonely" is an emotional state. It is a kind of sadness or melancholy. It is usually applied to people. "I am lonely" means not only that I am alone, but also that I would like to have some companionship. "Lone" is a simple statement of fact. It means something is isolated, single, separate, or unaccompanied. It would be common to speak of a "lone tree" or a "lone rock." In the United States the flag of the State of Texas features a single large star, and therefore Texas is "the Lone Star State." It does not mean that the star on the flag of Texas is sad and wishes it had other stars to talk to, it just means that there is a single star on the flag. In the fairy tale "East of the Sun and West of the Moon," we read: "So one day, when the White Bear asked what it was that she lacked, she said it was so dull and lonely there, and how she longed to go home to see her father and mother and brothers and sisters, and that was why she was so sad and sorrowful, because she couldn’t get to them."