Earlier, Lorenzo made landfall along the east-central coast of Mexico, southeast of Tuxpan, after rapidly strengthening into a Category 1 hurricane, the U.S. National Hurricane Center in Miami said.
Officials canceled classes and opened more than 60 shelters on the coastline of Veracruz state Thursday, as Mexico's government issued a hurricane warning from Palma Sola to Cabo Rojo.
At least 30 communities near several rivers were ordered to evacuate late Thursday. Residents scrambled to move furniture and belongings to higher ground even as roads began to flood.
"We never expected the hurricane would hit here," said Ribay Peralta, a 33-year-old lawyer who was packing his car with televisions sets, DVD players and other appliances in the town of San Rafael, a low-lying community about nine miles from Veracruz's coast.
"San Rafael is a town that gets flooded easily," he said by telephone.
The ports of Tecolutla, Tuxpan and Nautla were ordered to close by midnight, Veracruz's port authority said.
The mountain ranges and river areas in the Gulf state of Veracruz are dotted with villages connected by precarious roads and susceptible to disaster. Hurricane Dean brought widespread flooding to the area in August, and in 1999 a rainstorm caused floods that killed at least 350 people.
As of 0900GMT, Lorenzo was centered about 30 miles south-southwest of Tuxpan and was moving westward at 7 mph, the center said. It had top sustained winds near 65 mph.
The storm was predicted to cause "dangerous and battering waves" as well as storm surge flooding of half a meter to just over 2 to 4 feet, the center said. Forecasters said Lorenzo could dump 5 to 10 inches of rain in Veracruz, with isolated downpours reaching 15 inches).
Mexico's Interior Secretary warned of mudslides in at least four states and said port activity in the Gulf Coast states of Veracruz and Tamaulipas would be suspended.
Meanwhile, Tropical Storm Karen weakened in the open Atlantic Ocean.
Karen's center was about 755 miles east of the Windward Islands at 0900GMT and moving west-northwest near 10 mph. Its maximum sustained winds had decreased to 45 mph.