Can a figure have two lines of symmetry and no rotational symmetry?
Also a Rhombus. I turns out that Rhombus' can be closely related to the ellipses described above, and maybe shouldn't be seen as a truly separate phenomena:
inscribe a square in a circle. Pull two opposite corners of the square (and circle) outward or inward. The resulting figure is a rhombus inscribed in an ellipse.
In more than two dimensions this question can very interesting! But people are still getting PhD's describing these so I think it is not what you are asking about.