The state-run Rescue 1122 service responded to an emergency call and took Zahida (39) and Shamim (41) to Mayo Hospital after they were attacked in their residence in Ichhra area yesterday.
They sustained burns on the chest and arms, officials said.
Shamim told police that their neighbour Muhammad Amir and his accomplice entered their home and threw acid on them following a minor dispute.
Ichhra police station chief Ahsan Ashraf, however, said the women were engaged in a dispute with Amir and wanted to settle a score.
He said both sides had lodged a few cases against each other in the past.
Ashraf said a case would be registered only after receiving medical reports which established that the women had suffered acid burns.
According to police records, as many as nine women have been victims of acid attacks in different parts Lahore in the first six months of this year. One of the women died.