Most existing approaches for unsupervised bilingual lexicon induction (BLI) depend on good quality static or contextual embeddings requiring large monolingual corpora for both languages. However, unsupervised BLI is most likely to be useful for low-resource languages (LRLs), where large datasets are not available. Often we are interested in building bilingual resources for LRLs against related high-resource languages (HRLs), resulting in severely imbalanced data settings for BLI. We first show that state-of-the-art BLI methods in the literature exhibit near-zero performance for severely data-imbalanced language pairs, indicating that these settings require more robust techniques. We then present a new method for unsupervised BLI between a related LRL and HRL that only requires inference on a masked language model of the HRL, and demonstrate its effectiveness on truly low-resource languages Bhojpuri and Magahi (with <5M monolingual tokens each), against Hindi. We further present experiments on (mid-resource) Marathi and Nepali to compare approach performances by resource range, and release our resulting lexicons for five low-resource Indic languages: Bhojpuri, Magahi, Awadhi, Braj, and Maithili, against Hindi.