The best methodology to monitor the fishery in a lake depends on the goals of the study. What are the goals of the study? This guides the choice of what you measure, and in turn the best methodology.
Maybe asking the fishermen and check what is being sold on the market? This should already give you a basic understanding about how much is being caught.
I do not understand well from who or from thing exactly endemic species are threatened. Therefore, if the threat is overfishing, it is necessary to carry out an assessment of the resources fishable for management purposes. The methodologies are the same and much simpler of those used at sea, because the study area is closed. In a nutshell, the evaluation can be done through, if possible, direct survey (trawl surveys) or through indirect survey (catch-effort surveys). Particular attention must be paid to the sampling that must be, in both cases, statistically programmed in space and time. The mathematical models to be used for data processing and analysis, as a first approximation, can be both global models (based on cpue and MSY) and analytical models (like PseudoVPA and subsequently VPA). However it is of fundamental importance to know perfectly the life cycle of the species to be studied. After a number of years of study, if you have the necessary parameters, you can use mathematical models a little more sophisticated than the aforesaid, like bioeconomic and / or ecosystem models. The management recommendations will be based on the results obtained from the aforementioned analyzes. Ultimately, in my opinion, the best methodology to use for monitoring fishing in a lake is a catch-effort surveys by landing interviews that are statistically programmed in space and time.
All of your answers are very clear. They will be very usefull for our study. In fact, we are also monitoring the human dimention of the fishery (livelihoods, tradition...), the catch, the fish farming impact,...