I am not sure you will be able to represent the lake with SRTM data.
In easy words, SRTM data is bases on multiple Synthetic Aperture Radar imagery that put togheter can calculate heights. It is similar to photogrammetry and the more recent Structure from Motion methods: if the surface being sensed by the sensors is too texturally homogeneous, the algorithms strive to identify tie-points and calculate heights. An active remote sensor which is unable to "see" underwater, is unable to extract height data from stereo pairs. Thus, either a lot of interpolation will occur in areas of impossible extraction (water bodies, mountains, deserts) or "no-data" voids will be placed (that's the case in SRTM data).
But sometimes NASA fill the gaps by adding ancillary informations from other sources, you should check it!
Otherwise, you could digitalize the lake boundaries (shores) from orthophotos, georeferenced aerieal pictures or google earth imageries, then in ArMap you calculate the area of your lake shapefile, and the you calculate the volume by calculating Lake area times average depth (5m).
Obviously it is not an accurate volume, but depending on the use you want to do with it, might be an useful first broad idea!
If you don't have the bathymetry data to do this, get a boat with a depth finder, use your GPS for location and then take soundings with the depth finder by location. If you had a uniform grid of depths or just random depths, you can improve your estimate by creating subsurface contours. So that could be used in various ways to determine mean depth of the lake. As suggested if you have a mean depth, then you take the area of the lake times mean depth to get cubic volume in units you prefer, cubic meters, cubic feet, acre feet, etc. Developed lakes with dams are often located in a preferable spot to get the most lake for the dam, so you cannot look upstream or downstream topography that much. But if you if the lake was developed and you can find a pre-dam topographic map that might be helpful unless there has been an abundance of sediment that has come in over time to fill in portions of the lake. There are other more expensive methods that depend on how important this estimate is.
Since you want only shallow waters, you might use emergent vegetation as an indicator of generally water would be less than 2 m deep.
Sometimes on aerial photos, you can see differences in the water due to depth. These color changes might help you estimate depths, you might have to do some calibration with the boat and depth finder, GPS. Perhaps a good time to take a fishing pole too.
If you have a digital elevation model, I think you can convert that to raster pixels at 90m if you like. Most lakes have a low level or conservation level boundary, and average water level boundary and a high level boundary of not to exceed due to dam safety and need for release of flood water. Under any of these scenarios, you can define what you mean by shallow waters, and then using your raster pixels, determine how many of these are shallow and how many deep. So in the low level, you might have 50% of lake shallow at lake size A. At the average level, you might have 20% of lake shallow and lake size B. At flood stage, you might have 10% of lake shallow, and lake size C. If you have a drought, with water below the conservation level, that may be another scenario. You define the parameter of shallow, then count the pixels in GIS under the scenario that fits your circumstance. Unless you have very fine DEM contours, each pixel will probably have a elevation. If the elevation is less than the lake level, there is water depth. Only count pixels where the mean depth is less or equal to the definition of shallow water under whatever scenarios you decide to evaluate.