I'm trying to loft a sketch that would be starting on a curved surface and ending on a curved surface. 

I've attached a sample model of what I'm kinda trying to achieve. With a sketch of the actual profile of the dome.

Is there an easy way to have a sketch on the curved radius so when I loft it'll follow that profile? 

If not, I'll just cut the base flange where the tangent to the curve would be sketch my loft profile on that face and then perform the loft, I feel the cut is an additional step and ideally if I could avoid that it would be great. 

After I perform the loft I would be shelling the inside to make a uniform thickness of material. 

I'm open to any suggestions, thanks.