Non-alcoholic fatty liver disease (NAFLD) is a chronic condition characterized by disturbed carbohydrate and lipid metabolism and often complicated by psychoneurological symptoms, including anxiety, depression, memory deficit, and asthenia. Most studies of pharmacotherapy candidates for NAFLD focus on the ability of the tested drugs to restore the biochemical functions and morphology of the liver while their potential effects on the co-existing conditions remain overlooked. The aim of this paper was to investigate the effects of empagliflozin and L-ornithine L-aspartate (OA) on behavior, memory, and physical performance in C57BL/6 mice with experimentally induced NAFLD (6 months of a Western diet + weekly carbon tetrachloride injections). The disease affected animal behavior (locomotion speed decreased by 38% and 35%, p < 0.01; rearing increased by 432% and 279%, p < 0.05 etc.), induced long-term memory deficit (latency to find the target box increased by 108% in the Barnes maze, the number of errors increased by 439%, p < 0.05), and compromised physical performance (swimming time in the forced swim test dropped by 50%, p < 0.05 etc.). When administered during the high-calorie diet period, both drugs reduced anxiety (empagliflozin: the number of grooming bouts rose by 160%, p < 0.05 and 2173%, p < 0.01; time spent in the light compartment in the light/dark box test increased by 275%, p < 0.05, etc.; OA: time spent in the open arms of the maze increased by 267%, p < 0.05), and promoted memory retention in mice with NAFLD. OA improved physical performance (swimming time in the forced swimming test improved by 106%, p < 0.05, etc.). Thus, empagliflozin and OA can have a beneficial effect on cognitive functions, as well as behavior, and ameliorate asthenia in NAFLD.