In Pride and Prejudice, Jane Austen doesn't include references to the lower class. The closest she comes to including a lower class character is Georgiana's former governess, however a governess to an aristocratic young lady would certainly not be drawn from the lower class, as can be seen in her other work, Emma. Domestic servants, coachmen and footmen would more probably come from the lower class, but these characters don't readily enter into the storyline or plot of Pride and Prejudice. One can only infer interactions between the upper and lower class from Lady De Bourgh's conversation and from the few comments made about Darcy's care of the Pemberley estate.
Lady De Brough talks about her practice of knowing the family situation of those who live on her estate. These families and individuals would be the lower class laborers who farm Rosings estate and do other manual labor on the estate, such as caring for the horses and livestock. It is said of Darcy, and the former Darcy senior that they take meticulous care as benefactors of the lower class people living on the Pemberley estate.
Lady De Bourgh's and Caroline Bingley's behavior toward Elizabeth, Jane and Charlotte and their disparaging attitude toward Mrs. Bingley (not without sound reason...) shows a conflict between appearance and reality pertaining to upper class and middle class. Lady De Bourgh presumes to believe that these middle class individuals aren't worthy of respect due to upper class persons and thus interrogates Elizabeth. She also presumes that such middle class persons can't make sound decisions and therefore habitually instructs Charlotte on the management of her household. These attitudes and interferences cause theme-shaping conflict caused by being antagonizing and insulting due to perceived appearances contradicting reality, thus furthering entrenched pride and prejudice.