Yes, the technique vertical electrical sounding(VES) and electrical profiling (EP) are effective for erosion research. Just use these techniques respecting their specific criteria.
Geoeletrical methods can help only indirectly. In general the answer by Tomas Herman expoains the main aspects of this type of investigations.I can suggest to combine some gelogical, geotechnical and geoelectrical methods and to try to establish some correlation which cannot be universal but it can help for some case of analyses.
Sub bottom profiler is the best tool to know about the thickness of sediments deposit in the lake. However, you need to have suffcient water depth in lake to perform this survey atleast 3-4 m.
Bathymetry survey will give you the water levels in the lake. If you perform bathy survey every year you 'll get the knowledge of rate of sediment deposition every year.