Her article in thepeerage is here. According to that article, she refused to pay for this portrait.
Lady Manners wears a simple white (meaning aristocratic given how hard it was to clean garments then) with a long coiffure and a complex turban headdress in her 1794 Lawrence portrait.
Keywords: 1794, Lawrence, Catherine Grey Manners, British, long straight coiffure, turban, veil, vee neckline, criss-cross bodice, elbow length close sleeves, cuffs, waist band, close skirt, gloves, bracelets