iDash is an annual competition for creating new solutions to tackle the challenges of securing human genome processing in untrusted environments, such as the public cloud. In this work, we propose and analyze a simple but efficient candidate for the homomorphic encryption track of iDash 2022. We focus on different approaches for optimizing its homomorphic evaluation without any loss of precision compared to its cleartext evaluation. We represent our data inference model as a single large look-up table (LUT), which we homomorphically evaluate without model-specific optimizations. In this way, our results represent not only the model we chose but all others that could be represented as a LUT of similar size. We employ three different approaches for encrypting data that trade-off large ciphertexts (and, thus, high demands for storage and IO) and computational performance. We evaluate our solutions in two cloud environments similar to the reference provided by the iDash competition. As a result, we not only show the practicability of our solution in the context of iDash but also provide key insights on the practical issues of employing popular homomorphic encryption techniques, such as LUT evaluation, in a real-world scenario.