The rumours, linked to an upcoming requirement for councillors to take an oath of allegiance to the SAR, have prompted a wave of resignations.
Lo told an RTHK radio programme that more than ten of around 80 councillors from his party resigned on Thursday.
It has been reported that any councillors disqualified for past behaviour deemed unacceptable may have to pay their salaries back.
Lo said the rumours feel like “an ultimatum”, and some of the councillors from his party are still thinking about whether to quit or not.
He said everyone has different considerations, including the level of risk they can accept, and how much they could contribute to their communities if they stayed on as councillors.
Lo, who chairs Southern District Council, said the administration should come forward to explain the arrangements for the oath-taking and put a stop to all the rumours and guesswork.
He has also written an open letter to Chief Executive Carrie Lam, saying it would be unreasonable to recoup salaries and allowances from councillors who have been serving their constituents since last year.
He said stripping them of their seats would disrespect voters who put them in office and seriously undermine people’s confidence in the electoral system.