Welcome to the group, some details will help.
How big are we talking here? Is it 4" or 6-feet?
What is the worst surface finish you can accept?
Where is the "flat" between the hemispheres? Since you say it can't be done on a lathe, is it perpendicular to the pocket center-line?
If so, that brings in another round of complications.
Can you post a pic of what you are trying to achieve.
Generally, I will not give you the answer to your question, but I *will* guide you into discovering how to solve this yourself.