The deal would get rid of a key obstacle to passing updates to the North American Free Trade Agreement.
The White House had to decide by Saturday whether to slap tarifffs on autos over what it calls national security concerns.
The White House faces a deadline this Saturday to decide whether to slap duties on European car imports.
Pelosi and Lighthizer will address updates to the North American Free Trade Agreement and will likely discuss the widening trade war with China.
Trump, who campaigned on cracking down on unfair trade practices, has stirred trade conflict with China, Canada, Mexico and the European Union.
Trump also confirmed that he plans to meet with Chinese President Xi Jinping and Russian President Vladimir Putin at the G-20 summit in Japan in late June.
The move follows President Trump's decision to hike tariffs on $200 billion in Chinese goods.
U.S. trade talks with China ended early Friday afternoon with no deal, and Treasury Secretary Steven Mnuchin told CNBC there are currently no additional talks scheduled in the future.
It was not clear if discussions had ended completely for the day or if the vice premier would return for more negotiations.