Radius of curvature of a lens Is the radius of curvature of a lens correspond the the radius of the sphere in which the lens rises from?  
 A: Yes, one may see it like this:

Source: http://www.mydigitalphotographyclub.com/spherical-aberration.html
A: From this answer, I wish to make it abundantly clear to you that while one sphere can define two mirrors (concave and convex), it takes two spheres to define a lens.
In the case of a perfect concave or convex mirror,
 you can complete the sphere and by 
the definition of radius of curvature, the radius of the sphere is the same as that of the mirror. See figure below:

Now, in the case of lenses. 
Let us consider a common biconvex lense. The lense has two surfaces unlike a mirror which has only one. Each of these surfaces can be thought of as being a segment of a sphere as shown in the below figure:

The figure shows that the lens surfaces are part of distinct spheres and hence each surface has unique radius. Similarly, you can imagine a biconcave lens being part of two spheres.
Now, not all lenses are symmetrical like the above. the radii of lenses can be different from one another.
By different variations of the radii, the following lenses can be made:

PS: It is interesting to note that from the lensmaker's formula, it found that for an  asymmetrical thin lens, the focal length is proportional to the ratio between the product and sum of the radii:
$$f\propto \frac{R_1\cdot R_2}{R_1 + R_2}$$
