The blasts, on the island of Koulfoua on the Chadian side of the lake, struck a weekly market, the sources said.
No group has said it was behind the attacks, but the region is under a state of emergency after attacks by the Boko Haram militant group.
This year thousands of people fleeing the Islamist fighters sought safety on the island.
A police spokesman told Associated Press news agency that three women had carried out the attack on Koulfoua. At least 80 others were injured in the blasts.
Chad has played a key role helping Nigeria recapture areas seized by the group in northern Nigeria.
But as Boko Haram lost territory it stepped up attacks away from its Nigerian strongholds and into remote areas of Chad, as well as neighbouring Niger and Cameroon.
At least 17,000 people, mostly civilians, have been killed since 2009, when the group launched its violent uprising to try to impose Islamist rule in northern Nigeria, according to Amnesty International.
Three suicide attacks have hit an island on Lake Chad, killing at least 27 people, security sources have said.