An old-fashioned rap war that unfolded online at lightning speed has sent Kendrick Lamar to No. 1 on Billboard’s latest singles chart, while Taylor Swift easily holds off a challenge from Dua Lipa’s new album.

Relations between Lamar and Drake, two hip-hop giants and longtime rivals, exploded into a public war of words in recent weeks, in the form of a rapid-fire sequence of diss tracks packed with insults and unsavory (and unproven) accusations. Lamar seemed to get the last word with “Not Like Us,” released May 4, which becomes his fourth No. 1 on Billboard’s Hot 100 singles chart. That total counts collaborative releases — among them “Like That,” a track in March with the Atlanta rapper Future and the producer Metro Boomin, which kicked off the latest volley.

Consumption of “Not Like Us” was driven by streaming, with 71 million clicks in the United States last week. Another Lamar diss track, “Euphoria,” which came out the week before, is No. 3 on the latest singles chart, while Drake’s “Family Matters” is No. 7.

For this week’s Billboard 200 album chart, Lipa seemed to enter the contest with some advantages for “Radical Optimism,” her third studio LP. To promote it, she went on “Saturday Night Live” as both performer and host, and was on the cover of Time and Elle. Earlier this year, she had prominent performances at the Grammy and Brit award shows, and appeared on the cover of Rolling Stone.

But “Radical Optimism” was still trounced by the third week of Taylor Swift’s “The Tortured Poets Department,” which holds at No. 1 with a wide margin.

“Tortured Poets” had the equivalent of 282,000 album sales in the United States, including 298 million streams and 51,000 traditional sales, according to the tracking service Luminate. In its first three weeks out, “Tortured Poets” — which smashed records in its debut two weeks ago, despite mixed reviews — has racked up the equivalent of 3.3 million sales, including 1.6 billion streams for its 31 total tracks in the U.S. alone.

“Radical Optimism,” Lipa’s first LP since “Future Nostalgia” four years ago, which had ubiquitous dance-pop hits like “Don’t Start Now” and “Levitating” — and since Lipa’s hit “Dance the Night” from the “Barbie” soundtrack — had the equivalent of 83,000 sales and opened at No. 2, Lipa’s highest-ever chart position.

But the overall numbers for “Radical Optimism” were surprisingly low for a heavily promoted project by a major act. In its first week, the LP had 51,500 traditional sales — among them for 20 configurations on physical media, including 11 colored vinyl variants — and a very modest streaming take of about 40 million clicks. The chart performance of the album’s first two singles were indicators: “Houdini” went to No. 11, while “Training Season” stalled at No. 27.

Also this week, Morgan Wallen’s “One Thing at a Time” is No. 3 and Future and Metro Boomin’s “We Don’t Trust You” is No. 4. The K-pop ensemble Seventeen opens at No. 5 with a hits compilation, “17 Is Right Here.”