Isleworth is described as an "unlikely neighbourhood" because Dr. Thorndyke would not have expected of men of such means to live there. According to Wikipedia, Isleworth during Georgian and Victorian times had attracted many "aristocrats and high achievers" who built "many mansions and large houses". From this perspective, it would not have been strange for someone who wants to buy a £70,000 necklace to have a residence in Isleworth. However, railway expansion in the second half of the 19th century also brought factories to Isleworth, which may have made the town less attractive to the rich by the early twentieth century. ( _Dr. Thorndyke's Case-Book_ was published in 1923.)
Mr. Jacob Lowenstein had "secured the option" to buy the necklace, i.e. he had paid a nominal fee to ensure that Mr. Lionel Montague's firm would not sell the necklace to another buyer before he (i.e. Lowenstein) had decided whether he wanted to buy it or not.