Earlier in the day, the president had already lashed out at the local UAW president, David Green, saying he "ought to get his act together and produce".
GM didn't immediately respond to The Associated Press' requests for comment.
Roughly 700 workers from the Lordstown plant have already transferred out of state. More than 3,300 hourly workers were laid off indefinitely, representing about 7 percent of GM's hourly US employees.
GM reported near-record pretax profits of $11.8 billion for 2018, according to Fox News.
On Monday morning, Mr. Trump reiterated his support for the Lordstown plant to reopen quickly.
"Because the economy is so good, General Motors must get their Lordstown, Ohio, plant open, maybe in a different form or with a new owner, FAST!"
Earlier in November, General Motors announced plans to cut 15,000 jobs and close manufacturing plants in Lordstown, plants in MI, and Ontario, Canada.
The carmaker said it has placed more than 1,000 employees from so-called unallocated plants to other GM factories, adding that it has "opportunities available for virtually all impacted employees".
Mr. Trump praised Toyota for its investments in the U.S.in an apparent attempt to depict GM as being less committed to its home country than the Japan automaker.
Trump is expected to visit OH this week.
Trump prevailed in OH in the 2016 election, a win that helped him win enough electoral votes to become president despite losing the popular vote to Hillary Clinton.
Less than 24 hours later, President Trump sent out another tweet discussing the Lordstown GM plant, this time specifically addressing a local union boss about the closure.
The latest series of tweets recall Trump's early political success when, as a candidate, he pressured furnace maker Carrier to keep jobs in the U.S. They also come as the administration is trying to mobilize Congress to ratify the President's replacement for the North American Free Trade Agreement.
For instance, he has publicly called upon Apple to shift most of its manufacturing from China to the US, but the Silicon Valley company continues to make its iPhones and most other products overseas.
A small portion of the laid-off workers have found jobs at other GM plants far from the OH plant that was closed.
A fellow Republican from the Valley is agreeing with President Trump's call for GM to find a way to put the Lordstown assembly back in business.