After around two hours of in-chamber proceedings before Justice Manmohan Singh, no settlement could be arrived at between the two sides, senior advocate Aman Lekhi, representing Sharma, told the media.
The matter will now be taken up for hearing tomorrow by the court.
The court had yesterday asked both Lamba and Sharma to appear before it today "with an open mind" to resolve the issue. The direction had come when the court was hearing a petition filed by Sharma against his suspension from the House on March 31 for next two sessions.
He also said that a draft of a unilateral apology to be tendered by Sharma was brought by the other side, but the BJP legislator refused to accept that.
Lekhi further said that the decision of the Delhi legislative assembly to suspend Sharma was "illegal, arbitrary and malafide".
Sharma had moved the court now as a two-day special session of Delhi Legislative Assembly has commenced today.
Referring to a report of an Ethics Committee of the Delhi assembly on the issue, the government had said that Sharma was given chances to express regret on his remarks but he had refused.
The Ethics Committee had earlier "unanimously" recommended stripping Sharma of his membership for his remarks against Lamba and being "unrepentant" about it.
Sharma had earlier said "my intention was not to hurt Lamba as she is like my sister, but if she felt offended I express regret over it".
