It was a bomb that could essentially destroy Qo'noS, wiping out the heart of the Empire, killing billions, and in one shot ensuring that those rampaging fleets would suddenly become homeless needing to look to basic survival instead of conquest. While Earth was under direct threat, the majority of the Federation was still unoccupied, the cloaking advantage had been nullified, and now the Klingon Houses were the ones who could not afford any losses as most of their power had just been obliterated.
The Klingon Empire has always been portrayed as Qo'noS having much more importance to the Empire than Earth does to the Federation, even as the capital and Starfleet HQ. If, say, the Moon suddenly blew up devastating the Earth's environment so that most of the population would have to be moved for survival, this would be a problem for the Federation and Starfleet, but they'd survive. When Praxis blew up in Star Trek VI it was an existential threat to the Empire at such a level that they had to make a permanent peace because they wouldn't have the resources to fight the Federation if war broke out.
As for L'Rell, she was convinced the war would go on because her people were more concerned about personal glory and were winning. T'Kuvma had not started the war to win, he'd started it to unify the Klingons. Actually winning was secondary to his goals. L'Rell had seen what she'd believed in shattered, and with Voq's death, was the only one who still believed in that goal of unification. She was "fine" with it only because she was resigned to it, believing that nothing could be done to change it. The bomb gave her the opportunity to change things, to focus on the thing T'Kuvma considered most important: unification. The Klingons wouldn't change voluntarily to unite, so she was going to force them to change.
