Lakin, 76, lived in Jerusalem and worked as a teacher teaching both Jewish and Arab students and promoting for many years the ideal of co-existence.
Since his father's death, Avni has led the legal battle against Facebook and other social media sites.
Avni has sued Facebook for a billion dollars, given a speech on human rights at the United Nations, and met with US Vice President Joe Biden. Avni has also been key in advancing the "Facebook Bill," which has been nicknamed the "Lakin Law."
The proposed law would allow Israeli courts to order the removal of online incitement on Facebook, including advertisements, and would declare all incitement to be a criminal offense if it endangered a person, community, or the State of Israel.
It would also remove responsibility for dealing with incitement from Facebook, since the social media giant "sits with folded hands even after incitement has been published, and waits for a third party to sue the company in court."
Most of the cases of online incitement are clear-cut, with obviously hateful messages calling to kill, harm, or otherwise injure Jews or Israeli citizens.
"Facebook and Google are directly responsible for the content displayed on their sites. It is impossible to claim they rely on outside parties," Avni said. "When it comes to pornography, they don't wait for people to complain, right? They remove it immediately, and block users who violate their policy.
"They need to do the same thing with incitement to terror attacks. If they don't take down incitement, they should receive large fines. They should not be waiting for someone to sue them in court," he concluded.
Watch: Arutz Sheva spoke with Avni a few days after the murder of his father