Topic modeling plays a vital role in uncovering hidden semantic structures within text corpora, but existing models struggle in low-resource settings where limited target-domain data leads to unstable and incoherent topic inference. We address this challenge by formally introducing domain adaptation for low-resource topic modeling, where a high-resource source domain informs a low-resource target domain without overwhelming it with irrelevant content. We establish a finite-sample generalization bound showing that effective knowledge transfer depends on robust performance in both domains, minimizing latent-space discrepancy, and preventing overfitting to the data. Guided by these insights, we propose DALTA (Domain-Aligned Latent Topic Adaptation), a new framework that employs a shared encoder for domain-invariant features, specialized decoders for domain-specific nuances, and adversarial alignment to selectively transfer relevant information. Experiments on diverse low-resource datasets demonstrate that DALTA consistently outperforms state-of-the-art methods in terms of topic coherence, stability, and transferability.