Canadian Foreign Minister Chrystia Freeland said she was pleased with progress so far and Mexican Economic Minister Ildefonso Guajardo said the three countries are on the "right track" to reach a deal.
Lighthizer's reaction is now key.
Freeland said she hoped the United States would come to the negotiating table on softwood lumber, which is a separate issue from the NAFTA talks.
There are no talks scheduled beyond March. They suggested he shared others' increased sense of optimism - but might couch it in crotchety language.
There is also realization among many lawmakers who had in the past opposed the free trade deal that scuttling it would cause even bigger problems, she said. "We're starting to see that bond becoming more important than price for where countries are buying grains", said Karl Setzer, risk management team leader for MaxYield Cooperative.
"He recognizes there's a great deal of work to be done, but he's hopeful".
Several officials said the current week-long round in Montreal has been more constructive than past rounds as countries dive into a new back-and-forth about auto rules, dispute resolution, and a five-year review clause.
This round represented a new phase of the negotiations.
The almost concluded round in Montreal featured a new back-and-forth dialogue on autos and other major sticking points.
Flavio Volpe, president of Canada's Automotive Parts Manufacturers Association, said the Trump administration would not be selling out its base by agreeing to focus on the value of high-tech in autos.
As the negotiations grind on, officials are looking at an extra round in Mexico at the end of February, according to sources close to the process. The letter asserted that what US negotiators seek would eliminate American competitive advantages, "reducing sales, production and exports and harming USA workers in the process".
"I don't want to get overly optimistic with you - but there's just an air of optimism".
Freeland discussed Canada's counter-proposals with Lighthizer in Davos, Switzerland, on Thursday.
Greenwood said NAFTA enjoys bipartisan support from USA lawmakers from across the country.
US lawmakers see the renegotiation as a ideal opportunity to modernise the 24-year-old accord, Greenwood said. It views the investor-state system as an inducement for companies to outsource to Mexico, by providing additional legal security through a forum to sue for unfair treatment.
Lighthizer's comments were tempered by his assertion that Canada's wide-ranging complaint this month against the U.S.in the World Trade Organization amounts to a "massive attack on all of our trade laws".
With just eight weeks left in the current schedule of talks, unfolding under President Donald Trump's persistent threats to blow up the deal, the US administration has important decisions to make about NAFTA's future.
-Canada and Mexico could sign a side-letter or annex to cover their co-operation on the subject in the agreement. Richard Lugar, R-IN, said people need to find ways to inform the president on some issues, the Hagstrom Report said.
This "unprecedented" and "frivolous" action "does make one wonder if all parties are truly committed to mutually beneficial trade", Mr Lighthizer said.
Officials who have been meeting at a downtown Montreal hotel since January 21 managed to finish work on anti-corruption provisions in the treaty.
"I think the signal here is probably the Canadian proposal is so good for industry, and you'll hear from all the industry commentators, that it might be hard to say that that idea came from somebody else".