Instead, they drove into raging floodwaters, got trapped in their sinking truck on Interstate 95 and barely escaped.
"It was dark. It didn't seem like I was going into an interstate, it seemed like I was driving my truck into a river," Lawson said Tuesday in the aftermath of Hurricane Matthew.
"I said, 'This doesn't seem right.' I put it in reverse to back up ... and within 30 seconds, it was (water) from my ankles up to my knees."
Lawson said she didn't think she would make it out alive, and so she began calling family and friends to say goodbye. She pushed her kids out through the window of the truck, one after another, begging strangers to save them.
"It wasn't grounded anymore. I could feel this Dodge Ram on 26-inch tires floating," she said.
The mother and her children managed to escape, but they lost almost everything.
The truck had belonged to her late husband, a Philadelphia firefighter. Lawson was on her way to Florida with her husband's belongings -- many of them of sentimental value. He died of cancer last month, she said.
'I'm just lucky to be here'
Two days after their narrow escape, Lawson and her family were at a shelter in Lumberton, pleading with strangers for a ride to the bus stop so they could go home to Philadelphia.
As she waited, she held on to her children. She had a few items salvaged from her husband's truck: a picture of him standing near a fire truck, another of him in the military and his high school diploma.
The fast-running waters destroyed much of his possessions, including his will and the truck, Lawson said. "I'm just lucky to be here. ... I'm glad I'm here with my kids," she said. "I'm depressed, I'm stressed. ... I just wanna go home."
Most of Matthew deaths in North Carolina
The area where Lawson sought shelter has been badly hit by flooding after Hurricane Matthew struck parts of North Carolina over the weekend. More flooding is forecast for some riverside towns in the state, where boats and helicopter crews have rescued thousands.
Of the 30 deaths blamed on Matthew nationwide, 20 were in North Carolina, state authorities said Wednesday. Major rivers in the state are expected to be above flood stage through much of the week. CNN meteorologists predict Kinston will be one of the next towns to be flooded.
Many roads remain impassable, including a stretch of I-95 near Cumberland, Gov. Pat McCrory said.
"If we say the water is coming and we say do not drive through that water, we mean it," McCrory said.
The storm hurt agriculture and the poultry industry, too, with more than 100,000 chickens killed by flooding in Wayne County, said Kevin Johnson, county extension director.
"The situation is grave," he said in a news release. "There is also damage from wind. Many barns, sheds, buildings were damaged. Now farm equipment could be lost to flooding. We've got a long road ahead."
Floodwaters rising fast
The federal government has declared disasters in 34 of North Carolina's 100 counties, McCrory said. The declaration allows federal aid to supplement state and local recovery efforts.
Authorities went door-to-door to let about 500 people in the Black River basin know a mandatory evacuation had been ordered.
"A lot of folks in the flood area have been without power, so they have no idea what's coming toward them," said Tammy Proctor, spokeswoman for Pender County emergency management.
She estimated floodwaters were rising 3 to 5 inches per hour.
In Lumberton, one person died after being shot by a sergeant with the North Carolina State Highway Patrol, authorities said.
The sergeant and two Robeson County sheriff's deputies were conducting search-and-rescue operations Monday when they encountered a man in a flooded section of town, the State Highway Patrol said in a statement.
The man "became hostile toward the officers and displayed a handgun," prompting the sergeant to shoot him, it said.
The trooper, identified as J.F. Hinson, was placed on administrative duties. The person killed has not been identified.
Deaths in other states
Across the state, about 76,000 customers remain without power, McCrory said. Some 3,800 people remain in 46 shelters. Both those figures have dropped sharply since the first of the week, and local officials say local efforts are changing focus.
"This is no longer a rescue mission," Fayetteville Fire Department Battalion Chief Mike Martin said. "We have transitioned to a recovery mode of operation and damage assessment."
While North Carolina reported most of the deaths from Matthew, Florida said four people died as a result of the storm, and Georgia and South Carolina had three fatalities each.
The US deaths came after Matthew devastated parts of the Caribbean, killing more than 300 people in Haiti, according to Paul Altidor, the nation's ambassador to the United States.