The New Guy
Join Date: Dec 2011
Location: Down south, where the food is good.
So you want a spherical clock, with a turned base to set it in, but you don't want to turn the base and drill a hole to set it in? Sounds like you just don't want a turned base to me. The ones you have pictured above aren't turned bases. If you're looking for something like those, then I'd suggest avoiding the lathe as there are better tools to use. Table saw and router come to mind.
If you do want to turn the base, then your own imagination is the limit. Make something like a stemless goblet to set the sphere in, or a normal stemmed goblet, or a bowl shape, or well, whatever you can think of. Then you'll have to drill a hole, or turn a hole, to set clock in. Not sure of any way to avoid that.