HONG KONG—Pro-democracy lawmakers shouted down Hong Kong leader Carrie Lam and forced her to deliver an address by video in which she promised billions of dollars in social-welfare initiatives but resisted the political demands of antigovernment protesters who have disrupted the city for more than four months.

Twice Mrs. Lam went to the podium of the Legislative Council to deliver her annual policy speech, only to be interrupted by opposition lawmakers’ chant of “five demands, not one less,” a popular protest slogan. The same...