Authorities are focusing their search in a wooded area near a mobile home park in Gardendale, about 15 miles north of Birmingham.
The identities of the three murder victims have not yet been released, but police have confirmed that all were adults. Authorities urge anyone who sees him to consider him armed and unsafe.
Lever who also lived in Florida has an extensive history of arrests, Daily News reported.
Police in Gardendale, Alabama, have identified the man as a suspect in the fatal shootings of three adult relatives on Wednesday morning.
Lever was booked in Santa Rosa County in 2015 for an out-of-state fugitive warrant that originated from York, Pennsylvania on charges related to a child sex crime.
Police Chief Mike Walker identified the dead as 50-year-old Dana Reeves Lever, Kenneth Lever's ex-wife; her sister, Bonnie Reeves Foshee, 65, and Bonnie Foshee's husband, 69-year-old Don Austin Foshee.
In both cases, Lever was charged with involuntary deviate sexual intercourse with a child, aggravated indecent assault of a child, indecent assault person less than 13 years of age, corruption of minors, and distribution of explicit sexual material of a minor.
Anyone with information about Lever's whereabouts is urged to call the Gardendale police at 205-631-8787.
Lever was believed to be driving a red Nissan Sentra rental vehicle with a Georgia license plate, police said, and he could be headed to the Florida Panhandle.
Dana Lever sought the protective order claiming the man was stalking and harassing them, records show.
At the time, Lever's wife ex-wife claimed that the man was abusing her 11-year-old daughter during unsupervised visitation. Lever was held on $100,000 bail in the first case and posted it, being released from York County Prison afterward. The girl had been seeing a therapist who reached out and informed the mother of some concerns.
'My daughter has a different disposition when she returns home, ' the woman wrote in the complaint. They say he could be headed to the Florida Panhandle. "She is very clingy to me and will not let me leave her".