Is it possible to make an arbitrary lake bottom generator?
A common method of generating realistic-ish 3d terrain is as follows:

Start with a square (as seen top-down), described by the lengths of it's side (all the same), and the height of each of the corners.

Divide each edge in half; for example, add a new point halfway between the north-west point and the north-east point; it's altitude will be the average of the altitude of the two existing points, plus or minus a random number.

Now add a point in the center of the existing square; it's altitude being the average of the north, east, west and south points you've just created, plus or minus a random number.

You now have 4 smaller squares. Repeat this process on the four smaller squares, then the smaller squares within that, and so forth.

You might want to manually do the first few points, tweaking it to get the shape you want, then leave the details to the algorithm. Your random number for the adjustments of the "middle point" heights should be proportionate to the length of the sides; for example, the random altitude adjustment might be a random number up to X% the length; then subtract half of X% of the length. Adjusting X% will give you an area that is more or less "pointy".