Imperative sentences beginning with let are different from other imperative sentences. Sentences beginning with let express ideas such as a suggestion, proposal, request, wish, determination, desire etc.
Direct: He said, ‘Let me go.’
Indirect: He requested to let him go.
Direct: He said, ‘Let’s take him to the doctor.’
Indirect: He suggested that they should take him to the doctor.
Direct: The police inspector said, ‘Let no one leave this room.’
Indirect: The police inspector ordered that no one should leave the room.
Direct: They said to us, ‘Let’s go for a walk.’
Indirect: They proposed (or suggested) that we should go for a walk.
Direct: She said, ‘Let the child go home.’
Indirect: She permitted the child to go home.
Direct: The child said to us, ‘Let me go home.’
Indirect: The child requested us to let him go home. OR The child requested us to allow him to go home. OR The child requested that he should be allowed to go home.
Direct: The girl said, ‘Let me have another helping of the pudding.’
Indirect: The girl expressed her desire to have another helping of the pudding. OR The girl requested that she should be allowed to have another helping of the pudding.
Direct: The sage said to his disciples, ‘Do not blame others for your failures.’
Indirect: The sage advised his disciples not to blame others for their failures. OR The sage enjoined upon his disciples not to blame others for their failures.
Direct: The captain said, ‘Let’s have a race and see who the fastest is.’
Indirect: The captain proposed that they should have a race and who the fastest was.
Direct: The boy said to his father, ‘Let me play now.’
Indirect: The boy requested his father to let him play then.