Having been researching the ancestry of the Neale family (Rose Neale married Richard Down, of Halliwick Manor House, Colney Hatch, Middlesex -- their son Henry Down married Meliora Lodington, daughter of Thomas Lodington and Ann Day), it has become clear that they are also married into the same Lincolnshire families as the Lodingtons of Lincolnshire.
In fact, Lt.-Col. George Maddison of Stainton-le-Vale, Lincolnshire (a grandson of Ralph Maddison, High Sheriff of Lincolnshire and Theodosia Newcomen -- their daughter Theodosia Maddison married Samuel Neale, of the Middle Temple), was in the 4th Regiment of Foot, which was the regiment Ens. Thomas Edward Lodington started his army career with (before transferring to the 53rd Regiment of Foot).
So it seems even though this branch of the Lodingtons moved to London, it seems they remained close to their Lincolnshire cousins.