No stranger to the cut and thrust of adversarial politics, he opened the encounter at last week's committee with fulsome praise of the council's sports strategy.
After a moment's silence, Willie Innes, Labour's education convener, hurriedly commended his own party for its vision and commitment. So there.
Broun-Lindsay, who served on the former Lothian Region's education committee, got really wired in with flattering tributes to outdoor education strategies and the decision to continue sending children to the Lagganlia centre, near Kingussie. A visit for councillors during the summer to sample the excellent facilities would be ideal, he advised.
"I recall a similar venture with Lothian education committee with Elizabeth Maginnis abseiling down." He smiled mysteriously as he reminisced. Whatever was he thinking of? "Some members of my party came down head first," he explained. Innes quipped: "There would be less damage that way."
As the political pace quickened, Innes condemned the Pounds 300 million the Tories had removed from education over the past three years. "Where is it?" cried Labour members. "I've no idea where the money is," Broun-Lindsay replied, taking the challenge. "I am not a member of the Government. If I had the money, I would not be here."
"You've just had a room done up," noted a majority member. "But it's not gold-plated," Broun-Lindsay replied.
Stepping up hostilities, Labour sought to back the Scottish Parent Teacher Council's petition on education funding, throwing out bait to you know who.
Since he obviously did not have the missing Pounds 300 million in his pocket, Broun-Lindsay sat stumm. In East Lothian at least, the Tory opposition has joined Labour in arguing for more funds for schools.