"I take personal responsibility for the party's defeat in all three wards in my constituency and offer to resign from all party posts and as MLA," Lamba, who represents the Chandni Chowk constituency, tweeted.
However, Lamba said she will continue to support and "provide strength" to Kejriwal.
Lamba does not hold any important post in the party. She was removed from the panel of its official spokespersons last year.
Earlier in the day, the AAP leaders including Deputy Chief Minister Manish Sisodia were huddled at Chief Minister Arvind Kejriwal's residence as the trends showed a poor show by the party.
The prospects of a "massive" defeat loomed large over the AAP, close on the heels of the bypolls for Rajouri Garden Assembly seat where the BJP-Akali Dal candidate won while the party candidate lost his security deposit.
Trends showed that AAP was trailing far behind BJP which has been accused by the Kejriwal led party of "corruption and mismanagement" during its 10 year rule.
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