Lone may replace lonely or lonesome but typically is as objective as alone.

// a lone robin pecking at the lawn

Some common synonyms of lonely are alone, desolate, forlorn, lonesome, lone, and solitary. While all these words mean "isolated from others," lonely adds to solitary a suggestion of longing for companionship.

// felt lonely and forsaken

In some situations, the words alone and lonely are roughly equivalent. However, alone stresses the objective fact of being by oneself with slighter notion of emotional involvement than most of the remaining terms.

// everyone needs to be alone sometimes