Hill and her Fugees bandmate, Wyclef Jean, paid tribute to Flack during her service in New York City on Monday, March 10.

In 1996, the Fugees released their cover of “Killing Me Softly With His Song,” a song that Roberta Flack made famous in 1973. It became the Fugees’ biggest-ever hit, and it rocketed Ms. Lauryn Hill, ...