Alone and Lonely
Alone can mean ‘without anyone else present’ or ‘without help’.
I sat alone. (Nobody else was present.)
I went alone.
I did the job alone.
The house stood alone on the hillside.
Alone can follow a noun or a pronoun. In this case it means ‘and no other’.
Smith alone can solve the problem. (= Smith is the only person who can solve this problem.)
To leave / let somebody alone is not to touch or interfere with him / her.
Leave me alone.
Lonely is an adjective. It means ‘without companions’. Lonely can also be used to refer to places without many people or which are not often visited.
A lonely village
When you are feeling lonely, you are feeling sad because you are alone.
I like to be alone for short periods, but after a few days I will start feeling lonely.