The anticipated tenfold increase in the number of strong gravitational lenses from upcoming wide-field imaging surveys drives the need for efficient automated detection methods. We assess the performance of three domain adaptation techniques -- Adversarial Discriminative Domain Adaptation (ADDA), Wasserstein Distance Guided Representation Learning (WDGRL), and Supervised Domain Adaptation (SDA) -- in enhancing lens-finding algorithms trained on simulated data (or real data) when applied to real observations from the Hyper Suprime-Cam Subaru Strategic Program. We combine domain adaptation techniques with classifier based on Equivariant Neural Network and find that: 1) the combination of ENNs and WDGRL domain adaptation method has a high potential of reducing the number of false positives; 2) the combination of ENNs and SDA improves the ability of the model to distinguish between the lenses and common false positives such as spiral galaxies.