So, let's see if I got this right: the main difference is leaf size where from largest to smallest is: H. salicifolia, H. lacustris, H. augustifolia?
I have another Hygrophila that looks like H. salicifolia -- it's a stow-a-way stem on a plant order I made. This mystery Hygrophila throws out purple-ish new leaves with reddish-yellow veins that mature to green with slight purple overtones. Is that consistent with H. salicifolia? At the largest leaf point, the diameter is 1/2 inch wide. I'll post a photo sometimes next week.
Thanks again.