Tamil Nadu Police said Keerthi Asir, 29 and his father Israevel, 55, of Alakudi near Sri Vaikuntam allegedly consumed some pesticide they had brought with them and fainted.
Though locals rushed them to the High Ground Hospital at Palayamkottai in Tamil Nadu's Tirunelveli district, they died without responding to treatment.
Police said Mr Asir had married one Sukanya, also a college lecturer at Cheranmadevi, a town in Tirunelveli district. She had filed a dowry harassment complaint, and an investigation was underway.
Mr Asir met the college management on March 3 after being asked to do so over regularisation of his service.
Following this, the two allegedly committed suicide.
However the college management said that they were not responsible for the extreme step taken by Mr Asir and his father and that it might be due to a family dispute.
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.