The way the sentence is written, it is optional.
It is a misconception that both the indirect object pronoun and the indirect object are required. Nevertheless, they are used together quite often. The redundancy is welcomed.
So, there's nothing wrong with the sentence, as it is written, and there's nothing wrong with omitting the pronoun.
That said, if the sentence were reworded to
A mi hermano menor le mandé que hiciera su cama.
the indirect object pronoun is required.
And, if no indirect object is provided, the indirect object pronoun is required.
Here are the
rules (see entry 5).