Lakhani next plays compatriot Parul Goswami, who beat qualifier S. Partheepan 6-3, 6-1.
In the other two singles matches, Indian wildcard Sowjanya Bavisetti beat qualifier Aishwarya Agrawal 6-2, 6-3 while wildcard Ankita Raina blanked qualifier Arantxa Andrady 6-0, 6-0.
Bavisetti now meets the winner of the first round match between sixth seed and last year's finalist Alexandra Kolesnichenko of Uzbekistan and India's Kumari-Sweta Solanki.
Meanwhile, Raina in the next round can run into top seed and last week's champion Emily Webley-Smith of England, who plays Indian qualifier Adnya Naik in the first round Tuesday.