Officials across the hard-hit area said it would be several hours before they could get out to begin search and rescue missions.
Downed trees blocking roadways were expected to be the biggest immediate challenge for rescuers.
In Vermilion Parish, just east of Laura’s landfall, the sheriff’s office gave a stark warning to residents before the storm hit.
A statement on the sherrif’s Facebook page read: “If you choose to stay and we can’t get to you.
“Write your name, address, social security number and next of kin and put it a ziplock bag in your pocket.”