Lucas Hedges' big scene feels like the key to Greta Gerwig's approach, I think. A confrontation that seems rife with comedic possibilities (and is initially so, with Saoirse Ronan's anger and their talk about her mother first) suddenly opens up another world for Lady Bird when she listens to his increasingly and movingly vulnerable plea, striking her with how someone so different in family background can have their own anguish that arises out of the background envied by her.
Even apart from the richly developed main supporting players like her family and best friend, everyone in Lady Bird's circle is granted by Gerwig a moment or more of empathetic grace note, often sharply comedic but always deeply humane. From the drama teacher, whose melancholy in the next scene after that Hedges one is achingly felt but never directly revealed in cause and effect (apart from a gossip tidibit) since it's outsides Lady Bird's knowing, to the pretentious love interest, whose assholeness is never absolved but complicated in her feelings when she catches a glimpse of his ill father she was told about earlier. Lady Bird's coming-of-age template may be "generic" in broad strokes, but its story is filled to the brim with such finely observed details of tender everyone-has-their-own-world understanding, that they surround and enrich Lady Bird's joyful moments and common heartbreak beautifully. 8/10