In a question-and-answer session, Ms. Lenz repeatedly pressed Mr. Biden about his past votes for the Defense of Marriage Act, the military’s “don’t ask, don’t tell” policy that forbade openly gay people from serving and his statement earlier this year that Vice President Mike Pence, known for his socially conservative positions, was “a decent guy.”

Mr. Biden sought to defend himself, reminding the audience in a steamy auditorium that he supported same-sex marriage before President Obama. “I didn’t have to evolve,” he said.

Then, before an audience of 700 volunteers, activists and voters, he called Ms. Lenz “a lovely person,” prompting her to reply, “just asking the questions people want to know.

Offstage after their exchange, she wrote on Twitter that Mr. Biden called her “a real sweetheart.”