Lake sediments preserve information about past air temperature and precipitation, providing critical, real-world targets to validate climate models. However, these paleoclimate data encode information about multiple climate signals as well as lake dynamics, which makes comparison of paleoclimate data and model output challenging. Proxy system models (PSMs), or forward models that translate climate variables into proxy data, are tools for mechanistically interpreting paleoclimate data. PRYSM v2.0 is a PSM for paleoclimate data archived in lake sediments. Foundational to the accuracy of the PSM is a comprehensive understanding of the modern lake system supported by observations and meteorological forcing. However, two obstacles exist. First, lake water isotopes are the target of many proxies preserved in lake sediments, but the PSM does not have a built-in catchment model to aid simulation of lake water isotopes. Additionally, calibration of uncertain model parameters requires observations and expert knowledge about the lake, yet many sites are unmonitored. Here, we advance PSMs for lake sediment archives by integrating a simple runoff-isotope module that can be adapted to any lake and reproduce the seasonal timing and magnitude of two mid-latitude lakes with contrasting morphometry, hydrology, and mixing regimes. Using multi-year observational datasets from the lakes, we conduct model experiments that require the PSM to make water temperature and water δ²H profile predictions when calibrated to a single observed profile, which mimics common observation collection challenges. For these lakes, we find that observations from the warm, ice-free season are most informative and constrain uncertain parameter values that best generalize to unseen data from other depths and years. Our framework for running and calibrating the PSM is available as open-source tools in Python, aiding the application of this PSM to the vast global database of lake sediment paleoclimate time series.