Calculating lake depth from DEM

Hi

I was looking for help related to finding the depth of a lake with a DEM. The only data sets I have are a DEM and a lake polygon. I am not sure if my DEM includes bathymetry. So, I was wondering how I can tell if my DEM has bathymetry and if not how can I calculate the depth of the lake. My DEM has negative numbers for ocean areas but not for lakes, if that helps determining if it has bathymerty I am not sure.