I would start by doing a 50% water change with same-temperature conditioned water right away. Lethargy and popeye are both symptoms of poor water conditions. Also, for some reason a lot of people think they need to move their betta to another container while they do water changes. This just puts more stress on the fish. Leave him in the tank and use a gravel vacuum or turkey baster to remove water and waste from the substrate at the same time.
What are your water parameters? Posting your temperature, pH, ammonia, nitrite and nitrate levels would be a big help.