The word "godhead" is incorrectly defined by the LDS church, and it was its correct definition that, years ago––when I was trying to understand the nature of God better––proved to be invaluable in disabusing myself of many of the incorrect traditions in the LDS church while simultaneously coming to understand many mysteries of God.
I don’t know what pops into the minds of others when they hear the word “godhead,” but what used to pop into my mind as a consequence of my LDS upbringing was a picture of a presiding council of heavenly beings consisting of the Father, Son, and Holy Ghost—three individuals who were one in purpose. But that’s not what “godhead” means according to Webster’s 1828 dictionary. Instead, “godhead” means:
1. Godship; deity; divinity; divine nature or essence; applied to the true God, and to heathen deities.
2. A deity in person; a god or goddess.
(The emphasis on "essence" is mine, just because I'm really loving that word this morning. Extra credit for looking up the 1828 definition on that one.)
The Lectures on Faith (and Lecture Fifth, in particular) are trying to describe “godship”—what makes God who he is and why who he is enables us to exercise faith in him. If you read the Lectures through the lens of the King Follett Discourse and other scriptures that make a distinction between the Father, Son, and Holy Ghost and with the incorrect idea that a “godhead” is some presiding council, they make no sense. That’s not to say that there isn’t “individuality” between those beings, the way we would normally consider “individuality.” There is, but not in this context. And that is why the Lectures relate better to passages like Mosiah 15–because those passages are also trying to communicate more about “godship” to us than the process of attaining “godship,” which can only be understood with different definitions for “Father,” “Son,” and “Holy Ghost.”
The Lectures on Faith (and Lecture Fifth, in particular) are trying to describe “godship”—what makes God who he is and why who he is enables us to exercise faith in him. If you read the Lectures through the lens of the King Follett Discourse and other scriptures that make a distinction between the Father, Son, and Holy Ghost and with the incorrect idea that a “godhead” is some presiding council, they make no sense. That’s not to say that there isn’t “individuality” between those beings, the way we would normally consider “individuality.” There is, but not in this context. And that is why the Lectures relate better to passages like Mosiah 15–because those passages are also trying to communicate more about “godship” to us than the process of attaining “godship,” which can only be understood with different definitions for “Father,” “Son,” and “Holy Ghost.”