Under the supervision and direction of Joseph Smith, in a collaboration that included Sidney Rigdon and likely many other leading elders of the Church, The Lectures on Faith were prepared for the School of the Prophets, and subsequently printed and added to the canon of the church in the volume previously printed as The Book of Commandments, but which was also called the Book of Covenants. The Section contained the Lectures "Of Faith" at the beginning in a section called "Doctrine" and contained the Revelations of Joseph Smith in the second section called "Covenants and Commandments." Thus, the book of Doctrine and Covenants was born.
The section of doctrine published as scripture in the Doctrine and Covenants are not the entirety of the lectures given in the School of the Prophets. Rather the section worthy of publication are selected from those lectures. This gives the printed record a higher status as sacred scripture.
The question of authorship is moot, as Joseph the prophet shared and delegated responsibility for their creation and so doing took responsibility for their content, and edited and reviewed their publication. He writes, "During the month of January [1835], I was engaged in the school of the Elders, and in preparing the lectures on theology for publication in the book of Doctrine and Covenants, which the committee appointed last September were now compiling," History of the Church 2:180.
In 1921, the schism of the church that followed Brigham Young in the Succession Crisis, which had grown into the largest branch of the Restoration movement, removed this section from the Doctrine and Covenants, which, without changing the name, effectively returned it to being a book of commandments only.
The second largest schism, The Community of Christ, also removed this section, along with many other sections, on the theory that they had not been officially presented to the church for a vote, and could therefore not be in the canon.
While a sound practical theory for any organization burdened with being "official" the practical effect and error of this approach is essentially that creed and canon are oppressive and the safety of regulatory and democratic quality control is misleading. That while the church in one particular year can vote a revelation into the book, this can have no binding on people of subsequent generations for the same reason the vote was needed initially in a general conference of the church rather than a special committee. Each of us is free to discover and sustain for ourselves any revelations or books of scripture we wish without the sophistries of a church hierarchy, which admittedly consists of individuals who are spiritually advanced do not consist of individuals who are infallible or all knowing. It is their duty to teach on what they know or have had revealed, not on those things which have not been revealed to them.
Consequently, the practice is rightly to print or at least promote access to all of the revelations of the prophets and books of scripture and allow each member or investigator to decide for themselves. This objective may easily be facilitated by an explanatory note in the beginning.
Each of these organizations, without a revelation from the Lord, have removed parts of the revelations and holy scripture of God from the sacred books. Attempts to explain this by assigning authorship to Sidney Rigdon fail because he was a member of the First Presidency of the Church, called and appointed such and also called a teacher in the School of the Prophets under the direction of the prophet Joseph. He was authorized to receive revelation only in that calling and capacity appointed to him by Joseph. He is not found to be exclusively the author, but if he was, what he authored and used in the school was approved by Joseph for publication, and was reviewed and approved and sustained as scripture for this particular book by the prophet.
We should rather view the acts of these groups and their motivations and explanations as evidence of their apostasy. As efforts to establish a universally accepted creed and canon are hallmarks of apostasy in every era, and as such actions and intentions are never binding on the faithful who take their commandments from the Spirit and not flesh, we may safely ignore them.