The past tense of phrasal verbs, such as "let out" uses the same form as the past tense of the base verb - here "let".
The past tense and the past participle of irregular verbs (like "let") are listed in most dictionaries.
The past tense of 'let' is 'let'.
As far as I am concerned with the subject I would say that only let is possible. This is an irregular verb that has the same form for the present, past and past particilple - let.