Sentence that begins with let also belongs to imperative form. Sentence with let is slightly different form other sentences that give order, advise, warning, command etc. 

Rules

  1. Let is used in a sentence to express a suggestion or proposal. We have to understand from the mood of the sentence if something is suggested or proposed
  2. Reporting verbs such as ‘said’, ‘told’, ‘said to’ change to ‘proposed‘ or ‘suggested‘. 
  3. Here the reporting clause and reported clause can be connected with conjunction ‘that
  4. Sometime ‘to’ is used. In that case reporting verb ‘say to’ changes to tell.  
  5. ‘We’/‘us’ pronouns change to ‘they’. 
  6. If first person ‘I’ is included then ‘we’ or the mentioned pronoun remains unchanged.
  7. Modal auxiliary verb should is used in reported clause. 

Examples

Direct SpeechIndirect Speech
I said to my mother, “Let me do the work.”I told my mother to let me do the work.
He said, “Let us practice harder.”Mahu proposed to Shampa that they should watch a movie.
Mahu said to Shampa, “Let us watch a movie.”Mahu proposed to Shampa that they should watch a movie.
Father said to mother, “Let me do the cleaning.”Father told mother to let him do the cleaning. 
He said to me, “Let us be quiet.”He suggested to me that we should be quiet.
He said to her, “Let us buy a house.”He suggested to her that they should buy a house. 
I said to her, “Let us go on a travel.”I proposed to her that we should go on a travel.
Brother said to me, “Let us do our own works.”Brother suggested to me that we should do our own works.
The employee said to the boss, “Let me explain the matter to you.”The employee told the boss to let him explain the matter to him. 
The man said to the woman, “Let us eat in peace, without talking.”The man suggested to the woman that they should eat in peace, without talking.