Suspected members of Al Shabaab on Sunday launched an attack at Milihoi on the Lamu-Garsen road.
The militants burnt a lorry and an excavator belonging to H-Young construction company.
Lamu Police Commissioner Irungu Macharia confirmed the incident saying police engaged the militants in a gun battle before they (militants) fled into a nearby forest.
The police boss said the militants attempted to invade a police camp situated adjacent to H-Young camp.
No casualties were reported during the incident.
The attack comes slightly over a month after Al Shabaab militants launched attacks in the area notorious for terror activities.
On January 5, the militants attacked Manda airstrip in Lamu County leaving at least three American citizens injured and two others injured.
The airstrip is just next “Camp Simba” naval base that hosts US and Kenyan military troops.
Reports indicate that the militants were trying to access the base from the airstrip.
The Kenya Defence Forces (KDF) said in a statement that the terrorist attack was repulsed with five gunmen being killed.
Three people lost their lives after Al Shabaab gunmen attacked a Lamu bound bus on January 2.
The driver of the bus refused to stop and sped off, forcing the militants to shoot at the bus several times.
Following the increasing terror threats, President Uhuru Kenyatta ordered a sting operation to eliminate all militants in Kenya and its borders.