"let be 2. (intransitive, archaic) To stop, to stop doing something; to leave off (now used alone, formerly also + infinitive). Example: 1590, Edmund Spenser, The Faerie Queene, III.ii: 'Let be therefore my vengeaunce to disswade [...]'."
It can certainly stand alone.
The archaic form is fun! "I bade him to let be". I would really say "let [obj.] alone" and not use the word bade, but it doesn't really matter -- point made. The archaic form is certainly correct, though, even if some extremists might find that it is "not good English".
Thank you for your example: The archaic form is fun! "I bade him to let be". This will help me to never forget the word. Although many study Latin to understand English better, which is fine, I think many people would be shocked how much English comes from Danish, or is at least related to it closely. It's obvious their origin has a lot in common. Interesting.
Except, of course, that the Spenser citation may include my vengeaunce as a direct object, though one can't tell without the rest of the sentence. It is a construction that is common in a number of other languages, so I would not be surprised if it existed in English at some point somewhere, but I had never seen it. As I say, I'm still not sure I see it in the Spenser.
I asked a few native English-speaking friends of mine and they said that they have never heard the expression "let be" before. They say it may very well be in the dictionary but it is not in common literary or spoken use anymore. They would actually be inclined to say it is wrong, and recommend "let it be" to learners of English if they don't want to sound foreign.