In advanced metering infrastructure (AMI), the customers' power consumption data is considered private but needs to be revealed to data-driven attack detection frameworks. In this paper, we present a system for privacy-preserving anomaly-based data falsification attack detection over fully homomorphic encrypted (FHE) data, which enables computations required for the attack detection over encrypted individual customer smart meter's data. Specifically, we propose a homomorphic look-up table (LUT) based FHE approach that supports privacy preserving anomaly detection between the utility, customer, and multiple partied providing security services. In the LUTs, the data pairs of input and output values for each function required by the anomaly detection framework are stored to enable arbitrary arithmetic calculations over FHE. Furthermore, we adopt a private information retrieval (PIR) approach with FHE to enable approximate search with LUTs, which reduces the execution time of the attack detection service while protecting private information. Besides, we show that by adjusting the significant digits of inputs and outputs in our LUT, we can control the detection accuracy and execution time of the attack detection, even while using FHE. Our experiments confirmed that our proposed method is able to detect the injection of false power consumption in the range of 11-17 secs of execution time, depending on detection accuracy.