This is just a quick, off the top of my head way and may well be wrong.
In your viewport go to panels -> saved layouts -> Persp/UV Texture Editor
This will let you see whats going on better.
Select the sphere in your perspective viewport, go to edit polygons -> texture -> spherical mapping. Little controls will now show around the sphere and can be moved about to get the desired mapping. You will have to read/do a tutorial to learn these better.
As you move them you will be able to see the spherical UV map in the right hand viewport.
When finished go to UV snapshot and save the file out. This will be used to texture your sphere.
Add your texture to the image and save it ready for importing.
Finally add a new lambert material to your sphere and apply the newly painted texture to it.