Lawn & Alder were purveyors of all things fine for gentlemen and ladies in London. They retailed silverware, jewellery, spirits and wine, luggage and, as we see here, the occasional gun/rifle. Their wares were exported all over the British Trade routes. Like a small Aspreys (or a high-brow Army & Navy), the final address was just across from Asprey & Garrard in Bond Street.
Although the business started with some actual silversmiths, most of the items baring their name were made up in the trade and I suggest this is the case with the guns they retailed too.
You don't happen to know when they where in business? I was interested in how old the gun is.