Lambton is a village in Derbyshire. We are told that it is five miles from Pemberley House, most likely making the largest town in the estate's vicinity.
Lambton is described as “the scene of Mrs. Gardiner's former residence, and where she had lately learned some acquaintance still remained." The narrator does mention more than once that Elizabeth gets the opinions on Mrs. Gardiner's friends on the Darcy siblings, so there must be a number of people in the village still who knew Mrs. Gardiner.
As Darcy seems to have no trouble finding the inn where Lizzy and the Gardiners are staying, it is likely he is fairly familiar with Lambton.