It is clear in Sense and Sensibility that the character of Lady Middleton was created by Jane Austen to represent a typical sketch of the high-ranking, yet deeply shallow, ladies of the upper classes.
A cold, calculating, and exacting woman, Lady Middleton is still given some redeeming qualities such as her paused demeanor, her calmness, and her overall amiability. Yet, when it comes to classicism, and especially when it comes to loving otherwise shallow flattery, she reigns supreme. This is evident during her first introduction to the reader in chapter 6.
Lady Middleton had taken the wise precaution of bringing with her their eldest child, a fine little boy about six years old; by which means there was one subject always to be recurred to by the ladies in case of extremity, for they had to enquire his name and age, admire his beauty, and ask him questions which his mother answered for him...
Therefore, in order to be within her circle, two important conditions must be met: to be of rank, and to be willing to pay compliments to Lady Middleton and anything related to her. If only one of these conditions is met, she would still be friendly. Yet, both traits together will surely make her your best friend.
Further evidence of this lays on the fact that she is partial to the Miss Steeles over the Miss Dashwoods, even though the Miss Steeles are poor. What redeemed the two young ladies was the extreme amount of compliments that they paid Lady Middleton. This was the way for them to enter her society.
Additionally, Lady Middleton has no problem trying to become friends with Willoughby's wife despite of the pain that Willoughby caused Marianne. This is because all that she cares for is to mingle with social superiors and, since Willoughby only married for money, Lady Middleton must be quite clear that the lady in question is quite rich.
Therefore, as long as there is flattery for her otherwise shallow character and rank to satisfy her social climbing needs, Lady Middleton could prove to be a very good "friend".