Michael D. Coogan, The Old Testament: A Historical and Literary Introduction to the Hebrew Scriptures, third edition (OUP, 2014), 146-147.
[T]he book of Leviticus is a composite work. This is confirmed by the many editorial notes inserted throughout the text. The phrase “The LORD spoke to Moses” occurs over thirty times (and “to Moses and Aaron” another four times, in 11.1; 13.1; 14.33; 15.1; and once in 10.8, “to Aaron” alone). These variations may indicate originally distinct sources, as does the presence of several concluding statements (see 7.37; 26.46; 27.34).
It was P who preserved and edited the disparate traditions that comprise the composite work. As with the descriptions of the tabernacle and the ark in Exodus, P inserts into the sojourn at Sinai the rituals and practices of later times. P thus both preserves traditions from the Temple liturgies and also establishes a program for their restoration by the postexilic community in the late sixth century BCE and beyond. At the same time, however, Leviticus is not a consistent work, and it likely preserves traditions not just from the Jerusalem Temple but also from other sanctuaries throughout the land, as does the book of Psalms…even at the cost of some redundancy and inconsistency.