Not true about O'Brien. He was given his marching orders for his extreme views on Brexit and Trump:
MediaGuido had heard a few whispers about why James O’Brien had been canned by Newsnight – chiefly that BBC bosses were fed up with his Trumpian hyper-partisan attention-seeking both on their programme, on Twitter and elsewhere. One insider says they simply ran out of patience with him always going off on one.
He was a pain and people were delighted to see him go.
Pascal - he can have any position you like, he will still be partial to his own country and the power project that France and Germany started up. No one's saying he shouldn't be giving his views on the BBC. But it's essential to have an opposing view as something as important as Brexit. And it's interesting that the Armageddon prophecies of the Remain economists have not come to pass. There was barely a trickle of talent out of the City, and plenty coming the other way to continue to do business in London. So the Andrea Leadsome's got it right, even if they didn't have a flash title.
'MediaGuido had heard a few whispers'

Lamy wasn't giving his views about Brexit or the EU, he was stating facts about WTO terms, his area of expertise.