Fault diagnosis is one of the most important active strategies to protect lithium-ion batteries (LIBs) from safety accidents. The tasks of fault diagnosis usually can be divided into three levels, i.e., (1) fault detection, (2) fault isolation, and (3) fault estimation. The local outlier factor (LOF) method has been proved effective in conducting fault detection (level 1 of fault diagnosis) for LIB energy storage systems (ESSs). However, the original LOF algorithm (OLOF) may fail to make correct fault estimation (level 3 of fault diagnosis). Therefore, in this study, two novel LOF algorithms, i.e., the improved LOF algorithm (ILOF) and the simplified LOF algorithm (SLOF), are put forward to enhance the capability of fault estimation. The performance of the three LOF algorithms: OLOF, ILOF and SLOF, are firstly compared via three mathematical cases. Their capabilities in fault diagnosis are further investigated based on the simulated data from an air-cooled LIB ESS and the experimental data from a water-cooled LIB ESS. Results prove the effectiveness of all the three algorithms in fault detection; nevertheless, when the OLOF algorithm fails to make correct fault estimation, both of the two proposed novel algorithms, i.e., the ILOF algorithm and the SLOF algorithm, present the capability in making correct fault estimation. It is found as well that the ILOF algorithm is better than the SLOF algorithm in robustness though the latter is more efficient than the former in memory usage and computational time.