Written by Ambrose and Stu, “Supreme Ascendancy” comments on the lack of accountability towards organized religion, specifically the Catholic Church. Ambrose sings about how, despite being caught for numerous heinous crimes, religious leaders are continuously let off the hook due to their power and importance to religion and the public. He also calls out the tax exempt status of the church, and the hypocrisy of their teachings in the face of so many offenses, going as far as to say that Satan himself hides among the priests. The lyrics tear down the idea of “supreme ascendancy” by saying that nobody, regardless of belief, is above the law.
The song features a distinct 5/4 rhythm played by Cavs that the band riffs over to create one of the hardest rocking songs on L.W..

The song was performed by Ambrose (vocals/percussion/organ/keyboards/piano), Cavs (drums) and Stu (guitar/bass/vocals/sitar), with Ambrose playing the most parts out of anyone. He also co-recorded the song with Stu and Cavs (who did most of the recording for L.W.), and it was mixed by Stu. It was released as the second fourth on L.W. on February 26th 2021.