Question

He said," let me go out for a walk today."
Change into indirect form

Answer 1

he said that he wanted to go out for a walk

Answer 2

Understand the rules first :

Like Imperative sentences, use of 'Let' in the sentences of Let has different meaning and in Reporting Verb 'Said To' is replaced according to the notion of the sentence with words like - Proposed, Suggested, Requested, Ordered, Wished, Told, etc.

If the meaning of 'Let Sentence' is a suggestion, proposal or wish then for making Indirect Speech-
(1) 'Said To' is replaced with 'Proposed To / Suggested To / Wished To'
(2) 'Let' is replaced with 'Should'. 'Should' comes after the Pronoun. and
(3) 'That' is used to join both the parts of the sentence.

If the meaning of 'Let Sentence' is to allow, order or persuade then for making Indirect Speech
(1) 'Said To' is replaced with 'Requested To / Ordered To',
(2) 'Let' may remain in the sentence or it may be replaced with 'Allow' and
(3) 'To' is used to join both the parts of the sentence.

If condition or supposition comes in 'Let Sentence' then for making Indirect Speech
(1) 'Said To' is replaced with 'Told',
(2) 'Let' is replaced with 'Might' and
(3) 'That' is used to join both the parts of the sentence.

Answer :
-He requested to allow him to go out for a walk today.
-He wished to go out for a walk today.

Thanks !