Authorities found an inflatable boat off a beach at the popular resort of Costa Teguise with five bodies inside, a spokesman for the Guardia Civil police force told AFP.
Two migrants died after they got out while two others are in hospital in a "very serious" state, he added, though he did not know what the cause of death was.
He said that three of those who died "could be minors."
A further 18 migrants managed to make it onto the beach in Costa Teguise and were taken to the police station, he said.
"We suppose they came from the same boat" which arrived at the island around 1200 GMT, he said.
Emergency services confirmed the number of casualties.
Llegada de patera a Playa Bastián, Costa Teguise #LANZAROTE Servicios de emergencias en la zona confirman varios fallecidos. Continúa el dispositivo integrado por @CruzRojaEsp #SUC @salvamentogob @guardiacivil @polprcanarias y Policía Local— 1-1-2 Canarias (@112canarias) January 15, 2018
The Canary Islands archipelago off the coast of Morocco were once a prized destination for migrants hoping to reach Spain's shores and access Europe to begin new lives.
But migrants are increasingly favouring the so-called western Mediterranean trail which sees migrants making the sea crossing between north Africa and southern mainland Spain.
Since the beginning of the year, the International Organization for Migration says 285 migrants arrived in Spain via the Mediterranean, and 16 died during the crossing.
In 2017, more than 21,000 migrants came to Spain, and at least 223 died.