Trump said Mexico has been "totally great" in negotiating trade with the U.S.
Freeland's spokesman, Adam Austen, said Canada would only sign a good deal.
Asked about the challenges posed by a USA threat of auto tariffs, Trudeau said Canada would need to feel confident "about the path forward as we move forward - if we do - on a NAFTA 2.0".
Canadian officials said they do not believe Trump can rework NAFTA into a bilateral deal without the approval of Congress.
Lighthizer said the timetable for the new deal was set up so Pena Nieto can approve it before he leaves office on November 30 - an arrangement that's acceptable to Lopez Obrador.
U.S. President Donald Trump had already reached a deal with his Mexican counterpart, President Enrique Pena Nieto, in August.
Thomas Bollyky, a former US trade negotiator, said there is nothing legally stopping Canada from joining the trade pact after Congress receives the text. "And if we could do it in one deal, we'll do it as one deal - if we do it in two deals, we'll do it in two deals".
Mr. Trump again hammered Canada's dairy market on Wednesday, attacking the "300-per-cent tariffs" that keep USA imports out of the Canadian market.
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"The fact is, Canada is not making concessions in areas where we think they're essential", he said at the Concordia Summit in NY.
"On steel and aluminum ... we started off originally trying to have some kind of an overall agreement", he said.
The auto industry is key to Nafta and the free trade deal is critical to the North American supply chain.
"With Mexico, we're not going to say: "No deal" because of Canada", Lighthizer said.
"How do you sell a dairy product at 300 percent?" he said, adding that it is obviously Canada's way to back-door a trade barrier disguised as a tariff.
"I don't think there's anything to read into it", Mr. Trudeau said of the tepid greeting, adding he was just making the rounds of the table.
"I'm anxious a little bit that time will catch up with us", he said at a luncheon, noting that he had spent more time in Washington DC working on trade issues than ever before. "It was an interaction like so many are in the United Nations - quick but cordial". "We are very much looking in a positive and constructive way to getting to a renewed NAFTA that will be a trilateral agreement between Canada, Mexico and the United States".
"I'm anxious a little bit that time will catch up with us", he said, noting that he had spent more time in Washington working on trade issues than ever before.