LOS ANGELES — On “To Pimp a Butterfly,” Kendrick Lamar’s overflowing post-fame album, he was, in his own words, a king, a hypocrite, a sinner and a prophet. Awash in black music, black pride and shame, he attempted to propel the ghosts of Nelson Mandela, Tupac Shakur, Huey Newton and Michael Jackson through the will of his conflicted rhymes. “As I lead this army make room for mistakes and depression,” he warned at the end. Heavy was the head.

But on one afternoon in December, he was just content. Grinning, loose and nearly horizontal on the couch of his crew’s office, Mr. Lamar, 28, had reason to exhale: He was recently nominated 11 times in nine Grammy categories, including song (“Alright”) and album of the year (for the second time). In addition to being the most critically acclaimed album of 2015 and topping many year-end lists, “To Pimp a Butterfly” (TDE/Aftermath/Interscope) has also sold more than 750,000 copies and been streamed 375 million times, according to Nielsen, all without a hit single. Instead, the song “Alright,” which earned four nominations, has become the unifying soundtrack to Black Lives Matter protests nationwide.

“This album did what I wanted it to do,” a load-lightened Mr. Lamar said while wearing a hoodie that read “Compton,” his hometown, within the silhouette of the African continent. “That’s not necessarily to sell tons of records — though it didn’t do bad at that either — but to actually have an impact on the people and on the culture of music.”

The Grammy nominations are proof, he added. In 2014, Mr. Lamar infamously went 0 for 7 at the awards with his major-label debut, “good kid, m.A.A.d. city.” He insists those losses, including the one for best rap album to Macklemore, didn’t stick with him. (He did win two Grammys for the song “i” in 2015.) But that’s not to say he doesn’t want to win now. (The ceremony will be held Feb. 15.)