Despite what Hemingway said, probably more "modern American literature" comes from James than from Twain, including Hemingway's fiction. "Daisy Miller" is very early James (1878), but it already anticipates a lot of later writings.
"Daisy" was HJs' best-known work in his time, though more notorious than popular. Taken by many Americans to be "an outrage to American girlhood," because readers saw Daisy's behavior as immoral. That's of course the way the Americans in Europe in the story perceive her too. The first main section of the lecture was concerned with HJ's ironic point about how these Victorian-American descendants of the Puritans (Calvin from Geneva, like Winterbourne, and rebelling against "Rome," like Daisy) see bad manners as "evil," because they worship propriety with religious fervor -- a good example of this is the "service" in St. Peter's where Mrs. Costello, as a kind of pope, ex-communicates Daisy for going too far (p. 517). I talked about this as another instance of the way Realism sees "society" as playing the role "God" played earlier -- as with Huck's conscience.
The second main section: How "Daisy" is like and unlike Huck Finn. Twain & HJ disliked each other's work, but Huckleberry and Daisy have a lot in common, including the way their names evoke idea of natural-ness, vs. artificialities & deformities of society. But in HJ's version, this figure doesn't have a territory to light out to. Instead, comes east, into Old World, history, social circumstances, etc. Big shift in American literature registered by HJ -- from now on typical movement for characters, Dreiser's, Hemingway's, etc, is not westward, toward individual selfhood, etc, but eastward, to be measured by and against social circumstances.
"Daisy" an early, & schematic version of this story. Third main section: What HJ interested in using Daisy's life and death to explore. Her innocence affronts more complex reality represented, more-or-less symbolically, by "old world," Chillon (where innocence suffered) & Rome, especially Colisseum, where innocents got slaughtered. Real problem with her behavior (vs. verdict pronounced by ex-patriates in tale) is that she's too innocent, assumes reality as good-natured as she is. To HJ (& to many others) a kind of parable of America in modern world -- naivete undone by historical-social-environmental circumstances. HJ presents her story with some tenderness, but more ironic aloofness.
And in any case -- to get to last main section: Daisy herself not the center of the story. Rather, Winterbourne, who suffers from just the opposite problem -- not too innocent, but too much consciousness, atrophy of instinct. Cf. passages on pp. 487 & 491: Winterbourne "prepare[s] to rise" at Daisy's approach, & "lean[s] back in his seat" after "finding a formula" to categorize Daisy; his excess thought, as we see it in a passage like the long paragraph on p. 491, works to cut him off from life. Offered a Daisy in a garden, he fails to feel the chance for love until it's too late, until desire can only be married to regret. There are a lot of Daisy's in late-19th & early-20th C. American literature, but also a lot of Winterbourne's, including Eliot's Prufrock, Faulkner's Quentin Compson, etc. etc. And whole story economically states a kind of modern paradox without suggesting how to resolve it -- Daisy knows too little, Winterbourne too much; the first can kill you, but the second means that you fail to live.
In a typical 19th century fiction, Daisy & Winterbourne would end up getting married, and thus allow for a synthesis of the nature/culture or instincts/consciousness conflict. But like other Realists, HJ un-writing that romance convention (marriage as narrative & thematic closure). And like a lot of Modern literature, "Daisy Miller" is essentially about what doesn't happen: Winterbourne's failure to "get" Daisy, either to understand her, or to love her, and through love to live.