When she’s not busy building her namesake women’s and children’s clothing line and partnering with Stride Rite to design shoes, Lucy Sykes has apparently been embarking on another important mission: house-hunting. Sources say Sykes (half of the twin-sister pair who occupy an impossibly fashionable spot in New York society, the other half being Plum Sykes, the Vogue contributor and Bergdorf Blondes author) and her banker husband, Euan Rellie, may be needing more space, as they’ve been looking at townhouses all over Chelsea and the West Village, where they now live. (They have one child, and Sykes is pregnant.) Their most recent stop: a 4,800-square-foot, five-story house on West 22nd Street listed at $4.85 million. Those who’ve seen it say the 1838 Italianate mansion has high ceilings and original details like fireplaces, wide-plank floors, and plaster moldings. JC DeNiro brokers Christopher Mathieson and James Flowers, who have the listing, had no comment.