“Could it be possible that Mrs. Grantly had heard anything of that unfortunate Platonic friendship with Lucy Robarts?” Lady Lufton is at this point worrying about her son’s chances with Griselda Grantly, which seem to be diminishing, and wonders if the closeness between Lord Lufton and Lucy Robarts might have something to do with it. A Platonic friendship is one that involves no sexual/romantic feelings between the two persons involved. It is named after the Greek philosopher, Plato, who advocates love that is strengthened by an intellectual relationship. [JC 2005]
The ancients did not describe non-sexual/non-romantic relationships in this way, but the phrase is recorded in English in the 17th century. [RR 2011]
Sources: Plato, Symposium and Phaedrus.
“A slight cloud came across [Lord Lufton’s] brow as he saw this.” A sign of displeasure. In this case, Lord Lufton is unhappy to see that Lucy Robarts is snubbing him. See the gloss in the commentary for Chapter 24 of Barchester Towers. [JC 2005]