Lady Caroline Lamb was among the hundreds of female admirers who sent 24-year-old Byron an anonymous letter of praise for this autobiographical work about a disillusioned young man finding rapture in the natural world. “I think it beautiful. You deserve to be and you shall be happy,” she wrote.

As described in Antonia Fraser’s sprightly new biography, “Lady Caroline Lamb: A Free Spirit,” the aristocratic Lamb was better positioned than most to contribute personally to the poet’s joy, and she devised an initial encounter guaranteed to intrigue him. At a ball where Byron was surrounded by a flock of ladies, Lamb inveigled the hostess to introduce her, and, having looked earnestly, wordlessly, into the poet’s face, Lamb immediately turned on her heel.

Fraser maintains, credibly, that Lamb came up with her famous verdict on Bryon — “mad, bad, and dangerous to know” — years after this first meeting. Lamb was 26 at the time, and married to William Lamb, the future Lord Melbourne, prime minister and mentor to Queen Victoria. But she did not hesitate to fall into bed with Byron when he promptly pursued her.

Hewing to the enduring double standard, their coupling destroyed her reputation, but only added to the poet’s romantic mystique.

For Lamb, Fraser explains, Byron was a “great love, with poetry entwined around its very heart, for which her unfulfilled romantic nature craved.” Her husband, a remarkably tolerant fellow, and a talented politician, was a dull plodder by comparison.

Byron was likewise entranced — for a few months. The slight, lithe Lamb had enormous eyes, a pointed chin and, in an era of elaborate up-dos, wore her curly hair cut short. In a letter to her, he professed: “I have never knew a woman with … something of everything and too much of nothing, but these are unfortunately coupled with a total want of common conduct … then your heart, my poor Caro, what a little volcano! That pours lava through your veins.”

As Fraser tells it, the affair — with its masquerades, a mock exchange of vows, Lamb sending Byron a lock of her hair from an intimate place on her body — struck the poet as great fun until she turned up at his rooms on St. James Street and demanded they elope to the Continent: “We must go off together. There is no alternative!”

Here friends and family interceded to preserve the Lamb marriage. Caroline’s mother impelled her to travel to the family estate in Ireland, and Byron quickly moved on, taking up with Jane Harley, Countess of Oxford. “A mesmerizing courtesan” in Fraser’s words, who at nearly 40 could offer, the poet said, “autumnal charms.”

Lamb bombarded Byron with letters until he replied, “Lady Caroline — our affections are not in our own power — mine are engaged. I love another.”

What to do when your literary lover dumps you? Lamb made a few public scenes, upon returning to London, and then wrote a revenge novel, “Glenarvon.” This tale of betrayal, protagonists thinly disguised, was a wild success, which did nothing to soothe Lamb’s essential instability. She drank too much and took laudanum to excess. She died at 42.

In the prologue, Fraser, aged 90, concedes that this book is likely her last, “the culmination of an exciting and fulfilling life spent studying History.” (Note the uppercase H.) A meticulous researcher, and an agile, vigorous writer, Fraser has ascended the bestseller lists time and again with her vivid accounts of big lives — Mary Queen of Scots, Oliver Cromwell, Marie Antoinette.

This book’s smaller scope doesn’t suit Fraser — her study of Lamb never quite measures up to her previous biographies. (Although Fraser’s short memoirs “My History” and “Must You Go?” are absolutely charming.) But “Lady Caroline Lamb: A Free Spirit” is notable for its judicious restraint. Fraser wisely resists any temptation to hold up Lamb as a feminist heroine (which she was not), while acknowledging the constraints placed on her because she was a woman. She doesn’t pronounce a psychiatric diagnosis, although she points out that Lamb’s mood swings, racing thoughts and periods of depression suggest bipolar disorder.

Instead, Fraser embeds Lamb in the attitudes and prejudices of her time, while also describing her unquenchable need for attention, and the particular fulfillment she found in her affair with Byron, “a situation with immense dramatic possibilities.”

Lamb certainly believed, along with her contemporaries, that thwarted love produces madness. Did Lord Byron drive Lamb crazy, or was she crazy to start with? Fraser leaves the reader to decide.

Clare McHugh is the author of the novel “A Most English Princess.”

Pegasus Books. 224 pp. $28.95