There are many grammar books which suggest that we can change active voice into passive voice by using let, but when we consult the Oxford Advanced Learner's Dictionary, it refuses to form a passive sentence by using let. Why is this?
We can use the verb to let to form a clause in the passive voice, as in "Do not misunderstand me" (active) and "Let me not be misunderstood" (passive), but the verb to let itself has no passive voice. That is all that OALD (and every other dictionary!) tells you. Forming the passive imperative with let is not as common today as it was in the past. -- P. E. Dant
The short answer is that this use of "let" along with the passive "to be Xed" structure is considered outdated and is no longer in common use. It is likely that the books you mention are old-fashioned and do not reflect modern English grammar.
However, it is worthwhile for the advanced English student to be familiar with this, so that they can understand it when it appear in older documents, or media that use archaic structures to give the work the proper historical "feeling". For example, Yul Brynner as Pharaoh in the classic movie "The Ten Commandments" (1956)
People didn't really talk this way in 1956, but this kind of language feels archaic as if it was the way this ancient Egyptian ruler might have talked (had he spoken English, of course).
That being said, I would call this a conversion to the imperative, using the passive voice to avoid specifying who should do the action. This makes it suitable for things like religious texts, particularly those that specific things that should or should not be done. It gives the commandments a kind of historical gravitas, and the lack of specificity makes the command apply to everyone.
For example this (made up) scripture:
Let the cup be filled, and set on the table, and let no one drink from it, but instead let it be an offering to the Lord.
Again, I wouldn't recommend you use this grammar in ordinary conversation -- except perhaps ironically, as a kind of joke when talking informally with friends.