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Use North_America_Albers_Equal_Area_Conic projection for your digitizing file if the lakes are all over the continent.
WGS_1984_Web_Mercator_Auxiliary_Sphere for the file will give you very high areas increasing as you go north because of the cylindrical stretching distortion, but should be OK for the data frame although you can change that to Albers as well if you like. It should not change the areas.
If you use this in a geodatabase feature class the area is automatically calculated in a field.
Thank you very much for getting back to me with your advice, it has worked perfectly from what I can see so thanks for your input.
All the best