Sorry for the delay C.M.M.M.
First off, the words "cannot" and "can not" mean the same thing. Cannot is just more academically acceptable.
Second, you're right about what double negatives are, but this statement is not one.
"this translation to the state of justification" is the subject
"cannot be effected" is the predicate and together they form the clause. For this to be a double negative, the clause itself would have to contain double negation, but it does not. It would have to look like this to be a double negative: this translation to the state of justification
cannot not be effected without this or that...)
De Morgan's Law is the principle to apply in the negation of this compound statement.
According to De Morgan's Law:
NOT (A OR B) is logically equivalent to (NOT A) AND (NOT B)
This means that the statement is logically equivalent to this:
"...this translation, cannot be effected, without the laver of regeneration," AND "...this translation, cannot be effected, without the the desire thereof"
Simply put, only one of these needs to be missing for justification to be impossible.