Little in the text indicates that Lucas's reaction to Charlotte's engagement was socially inappropriate, but we do get a hint of Lady Lucas crowing excessively over her success in the following line:
Lady Lucas ...called at Longbourn rather oftener than usual to say how happy she was.
This might be considered inappropriate because Charlotte's fiance, Mr. Collins, was heir to the Longbourn estate, meaning Charlotte and Mr. Collins would, upon Mr. Bennet's death, have the legal right to immediately cast Mrs. Bennet and her daughters out of their home. Reminding Mrs. Bennet of this fact could be seen as insensitive, certainly not of the highest order of social graciousness. On the other hand, Mrs. Bennet had, through the earlier part of the novel, dished out rudeness almost constantly to Mrs. Lucas, bragging insufferably about her own daughters' prospects and making condescending remarks about Charlotte, a person everyone had written off as an old maid. More to the point, following WD Harding in his Austen essay "Regulated Hatred," both Mrs. Bennet and Mrs. Lucas used legitimate and socially acceptable conventions to savage each other without doing or saying anything overtly inappropriate.
If we look past the socially acceptable to ethically acceptable behavior, however, we might take offense at the following:
Lady Lucas began directly to calculate, with more interest than the matter had ever excited before, how many years longer Mr. Bennet was likely to live.
In other words, Lady Lucas is, privately, experiencing a certain glee or schadenfreude over the fact that her daughter will be mistress of her rival, Mrs. Bennet's, home. Using the terminology of our own time, we might say this is not cool.