Resignations of senior People's Action Party (PAP) members are rare in Singapore, where the party has been in power since 1959, before the city-state's independence in 1965.
Lee in a statement said speaker Tan Chuan-Jin had "fallen short" in the matter of his personal conduct and he understood his desire to step away from politics and "help heal your family". Lee did not elaborate.
The office gave no reason for the resignation of the other lawmaker, Cheng Li Hui, who has been in parliament since 2015. Cheng could not immediately be reached for comment and her Facebook page had been taken down at the time of the announcement.
The resignations were necessary to "maintain the high standards of propriety and personal conduct which the PAP has upheld all these years," Lee's statements said.
Singapore has been hit by a series of political fallouts of late. last week, transport minister S Iswaran and hotel tycoon Ong Beng Seng were arrested in a rare high-level graft probe. They have yet to give comment on the investigations.
Speaker Tan's resignation comes after a video clip appeared on social media for several hours during which he is heard insulting another lawmaker, apparently unaware his microphone was still on.
In his resignation letter, which was cited by Lee's office, Tan said: "I had made a mistake in parliament when I uttered words which were rude and unparliamentary."
(Reporting by Xinghui Kok; Additional reporting by Chen Lin; Editing by Martin Petty)
By Xinghui Kok
