Alone is a fact, it means that there is no one around. You can be alone in your home, alone in your ideas (alone with everybody) when no one agrees with you on something, but you are technically not alone, as there are other people around you. Lonely is about how one feels. You can be in park and lonely, at work, but with no one you can talk to, so you are lonely. As for the sentence, it can be written that way, but it does have slightly different meaning, you can be alone but not be lonely at the same time.

no, you can't say they are sad and alone."longly" means a feeling in their mind,but "alone" means just one person,no one company him/her~Hope these words help you

One can be alone, yet not lonely. One can be lonely, yet not alone.

Generally speaking, "Lonely" means sad, the one, who misses somebody, solitary. "Alone" means the only one, or without anyone else near, or without anyboby's help, on one's own. For example: "I have no friends, I'm so lonely" and "I'm alone in this room" (or "I did it alone, without anyone's help").