According to the Dune: House Corrino novel, she wanted to have a throne of her own next to her husband's Imperial Golden Lion Throne just like her father-in-law, the aging tyrant, Elrood Corrino IX had one for his second wife, the late Padishah Empress Yvette Hagal-Corino:
Anirul waited at the base of the dais, still looking up at him. “I want my own throne in here, beside yours, Shaddam- just as your father had one for his favorite wife.” The Emperor slurped half of his spice coffee to calm himself. Another throne in here? Though he’d assigned his Sardaukar spies to watch over Anirul, they had not found anything incriminating yet, and probably never would. The veils of the Bene Gesserit secrecy were not easily penetrated. He weighed possibilities and options. Reminding the Landsraad that a Bene Gesserit sat by his side might be to his advantage after all, especially as he stepped up his aggressions against spice hoarders. “I shall consider it done.” Then all of a sudden, Anirul snapped her fingers and motioned toward an arched doorway, where two Sisters appeared from the hallway shadows directing four stout male pages as they carried a throne into the audience chamber. Obviously built of the same substantial weight, the chair was smaller than the Emperor’s Golden Lion Throne, but it was finally constructed of the same translucent blue-green Hagal quartz.
But unfortunately, Shaddam refused to let it be on the top platform where his throne was and told the two pages to place his wife's seat far below on the left level so that the Empress won't try to manupilate him in public.
After the early dusk of her tragic death on Kaitain due to the birth of the young na-Duke Paul Atreides, Anirul's throne remained there in the Imperial Selamik-- the Imperial Audience Chamber during the night of her mummification and funeral pyre. As for the Emperor's point of view, he left it to his eldest daughter, the eleven-year-old Imperial Crown Princess Irulan Corrino I whom he'd selected as the Sovereign Co-regent of the Imperial House Corrino.