This study attempts to understand the asymmetry in the Indian Summer Monsoon Rainfall (ISMR) response to two types of La Niña whether they evolved from El Niño or La Niña in the previous boreal winter season. It was seen that nine La Niña years during the monsoon season were preceded by El Niño (hereafter ELLA) whereas eight were preceded by La Niña (hereafter LALA) during the period 1961-2021. India received more rainfall during the ELLA years as compared to the LALA years, linked to the difference in the Sea Surface Temperature (SST) and large-scale atmospheric circulation anomalies over the tropical Pacific and Indian oceans. Based on the strength and patterns of the cold SST anomaly and shift in the Walker circulation over the equatorial Pacific Ocean, the enhanced (weakened) convection over the Indian landmass during the ELLA (LALA) years, contributed to more (less) rainfall over India.