Was Picard lying? I think he might have been.
I don't think so. There's other dialogue in the episode that suggests things look bleak for the Federation. Tasha tells Castllo that Starfleet has lost more than half of its vessels to the Klingons. Now, that doesn't mean that defeat is inevitable, but it's certainly not a sign that the Federation is on the verge of winning the war.
Also, consider that as a captain, Picard likely had access to information that the majority of officers wouldn't. Everything about his demeanor during that scene suggests he's speaking with Garrett captain to captain, hoping to appeal to her desire to serve the greater good, even if doing so means sacrificing her ship and her crew.