Associate Professor Lynch last year refused to assist Dan Avnon, the author of the only joint civics curriculum for Jewish and Arab school students, to undertake work at the university as a representative of an Israeli institution.
Shurat HaDin, which models itself on the Alabama-based Southern Poverty Law Centre that has successfully used US courts to target the Ku Klux Klan, alleges the BDS movement is racially discriminatory and undermines human rights.
Shurat HaDin director Nitsana Darshan-Leitner said: "Lynch and his ilk seek to boycott Israeli and Jewish national products, whether it's goods, services, performers or professors. By singling out Israel and no other country, the BDS ... exposes the anti-Semitism that motivates them.
"We are hopeful that this historic proceeding against the BDS movement will serve as a model for battling it in other jurisdictions worldwide."
The Shurat HaDin lawyer who has lodged the claim, Sydney-born Andrew Hamilton, said the BDS campaign sought to "discriminate and impose adverse preference based on Israeli national origin and Jewish racial and ethnic origin of people and organisations".
"It does nothing to help Palestinians and indeed harms them," Mr Hamilton said.
He said similar legal actions had succeeded in silencing European BDS proponents.
"It's about time someone exposed the racist false narrative that is at the heart of the BDS movement in a legal forum," Mr Hamilton said. "Boycotting businesses and people just because they have a particular national, racial or ethnic origin is racism ... It is no more legitimate political protest than boycotting the local corner store to protest against Kevin Rudd's policies."
The Sydney University student union has backed BDS, despite fierce opposition from some quarters. The BDS movement compares Israel with apartheid-era South Africa, causing it to be condemned by bodies such as the Simon Wiesenthal Centre as anti-Semitic.
The Shurat HaDin complaint is based on Section 9 of the 1975 Race Discrimination Act. It reads: "It is unlawful for a person to do any act involving a distinction, exclusion, restriction or preference based on race, colour, descent or national or ethnic origin which has the purpose or effect of nullifying or impairing the recognition, enjoyment or exercise, on an equal footing, of any human right or fundamental freedom in the political, economic, social, cultural or any other field of public life."
The complaint also cites alleged violations of sections 16 and 17 and parts A and B of Section 18 of the act.
Mr Hamilton described the BDS movement as "anti-Semitic at its core". "When BDS protests feature both Islamist terrorist groups like Hezbollah and neo-Nazi groups, it is clear something is wrong," he said.
Associate Professor Lynch is on study leave and could not be contacted yesterday. Sydney University vice-chancellor Michael Spence previously has condemned academic boycotts of Israel, but said the centre and its staff were free to set their own policies.
A university spokesman said: "The university has not received a complaint from the Human Rights Commission. It would be inappropriate to speculate about hypothetical actions which might be taken in response to such a hypothetical investigation."