Northern Powergrid said its 11,000 volt lines in the Louth area had been targeted by a gang in a series of raids earlier this month.
As well as disruption to nearly 1,000 homes and businesses, live cables had been left trailing on the ground.
The company has offered a Â£1,000 reward for information about the crimes.
The thefts, near South Somercotes, Theddlethorpe and Welton le Wold, had caused Â£20,000 worth of damage, the firm said.
Thieves who have stolen 7.5 miles (12 kms) of high voltage cable in Lincolnshire are putting lives at risk, a power company has said.