Self-supervised learning has been known for learning good representations from data without the need for annotated labels. We explore the simple siamese (SimSiam) architecture for representation learning on strong gravitational lens images. Commonly used image augmentations tend to change lens properties; for example, zoom-in would affect the Einstein radius. To create image pairs representing the same underlying lens model, we introduce a lens augmentation method to preserve lens properties by fixing the lens model while varying the source galaxies. Our research demonstrates this lens augmentation works well with SimSiam for learning the lens image representation without labels, so we name it LenSiam. We also show that a pre-trained LenSiam model can benefit downstream tasks. We plan to open-source our code and datasets.