the quality of the interferogram seems good in general.
I wonder a bit why the valley in the center is still so present after topographic phase removal. The interferogram seems to contain much topographic contributions. The interferogram formation includes topographic phase removal if you activate it, can you please run it twice: one time with and one time without topographic phase removal and compare the results side by side? I recommend using SRTM 1Sec (AutoDownload)
The artefacts at the western border of the lake can probably be tackled by reducing Sigma to 0.6 during the Goldstein filtering.
The rest depends on how the modeling program deals with low cohernce areas. As you say, coherence will remain low over the lake no matter how you preprocess the data. Maybe the modeling software itself allows masking of such areas?