Here the 1905 LDS edition accidentally dropped the object pronoun him, but the 1920 LDS edition restored it. The text has four other instances of “desiring him that S”, where S is a finite clause:
But there are also six cases that could have the him but do not:
Since either reading is theoretically possible here in Ether 15:4, the one based on the earliest textual sources will be retained (namely, “desiring him that he would spare the people”).
Summary: Retain the object pronoun him after desiring in Ether 15:4 and wherever else the earliest textual sources support the reading with the object pronoun in the expression “desiring him that S”.