"lively question and answer" is a correct and usable phrase in written English.
You can use it to describe a discussion or dialogue where questions are asked and answered in a lively, engaging manner. For example, you could write, "The lively question and answer between the two debaters really held the audience's attention."
The presentation elicited a lively question-and-answer session, during which students asked about the N word, discrimination against white people and men, and the definition of "Asian".
Five days after a lively question-and-answer session with House Republicans at their retreat in Baltimore, Mr. Obama stood before a friendlier audience of Senate Democrats at the Newseum here.
An edgy confrontation between two male dancers, Mr. Leichter said during a lively question-and-answer session afterward, was about exploring the idea of two people competing to control each other.
During a lively question-and-answer period, Mr. Gates was pressed on whether the United States had a double standard in organizing the world community to prevent Iran from developing nuclear weapons but not working to disarm Israel.
During a lively question-and-answer period after the speech by Mr. Gates, Alexey Ostrovskiy, a member of the Russian Parliament, challenged the United States record in arming anti-Soviet fighters in Afghanistan — many of whom became Islamic extremists and members of the Taliban or Al Qaeda.
They toured classrooms and health facilities, and had a lively question-and-answer session with local leaders.
Both Ms. Veneman and Sir Roger addressed the opening of the summit and then held a lively question-and-answer session with the delegates.
A few more aspiring magicians were in the audience, at least as seen by a show of hands during the lively, and also quite funny, post-screening question-and-answer session with the cast and some crew.
"Such a lively debate," Mr. Argott said happily, describing the question-and-answer session that followed the screening.
And one engineer received lively applause when he told Ms. Fiorina during a question-and-answer session that "the thing that gets hit first" in the rush to meet the company's quarterly financial targets "are those new ideas".
Following a lively and engaging question and answer period between the American women and the women from Kav Mashve, and just before we were due to adjourn for dinner, I discussed with those assembled that for so very long now, men have been in charge of nations and governmental relations in the Middle East with little success in bringing about a comprehensive and lasting peace.
