Alone means “by yourself” – there is nobody else with you:
- I like to take long walks alone so that I have time to think.
- He got up and left the restaurant, leaving me alone at the table.
Lonely means “feeling sad and isolated” – it is a negative emotion.
- I was lonely on my first day of class because I didn’t have any friends.
- She can’t stand being single; she says she feels lonely without a boyfriend.
Only means “just one” and can be used with people, objects, or actions. After the word only, we must have a person, object, or action.
- Dana was the only student who understood today’s English lesson.
- I have only one pair of sunglasses.
- I didn’t have a lot of money, so I only bought this T-shirt.