The petition referred to a move, allegedly by the union's leaders, to appoint Mr Kadirval, who is known also as T Velu, as a cadre member even though he was voted out at a branch election.
It was addressed to Manpower Minister Ng Eng Hen and copied to several other government and NTUC leaders, including Mr Lim.
Last month, lawyers acting for Siasu general secretary Mohd Hussain Kassim and executive council members sent a letter to one of the petition's organisers, and called the allegations 'totally untrue and unfounded'. And this month, lawyers acting for Mr Kadirval sent a similar letter to several others who signed the petition.
Among other things, the letters said the claims in the petition constituted 'a most serious and damaging libel', demanded a letter of apology to be published in the media, and sought damages.
Talking to reporters on the sidelines of the NTUC Workplan Seminar, Mr Lim said that in general, 'union leaders are here to serve the interest of the workers. Our workers must respect the leadership of the union leaders'.
He said NTUC was in no position to judge whether the accusations of the members or leaders were warranted, justified, or accurate as it was not present at the union's meetings. But he had strong words for both groups: 'On the part of the union leaders, using union funds to sue the workers, what's there to gain for the unions?
'On the part of the workers, if there's any disagreement with the action of the union leaders...getting hundreds of workers to sign up and to get involved with such litigation to the extent where, at the end of the day, they may have to sell the house, sell the car, to pay for the legal fees and so on, I will say who gains?
'The lawyers. The lawyers of both sides, regardless of the outcome of this suit, will gain. But I see no gain for the union, I see no gains for the members.'
Mr Hussain and Mr Kadirval declined to comment when contacted, saying this was an internal matter. Several members who received letters from Mr Kadirval's lawyers also declined to comment.
But ex-Siasu president Eddie Chew, who stepped down last year, agreed with Mr Lim that both parties should work things out. 'It would be good if NTUC comes in and gets them to stop,' he said.