You can freeze pretty much anything inside a clear ice sphere using Directional Freezing, the technique I pioneered here on Alcademics.
As I've written previously, to make clear ice spheres you can use directional freezing with an ice ball mold on top of a thermos-style insulated container.
Fill both the ice ball mold and the container with water (I use filtered water; no need to distilled or anything). Place the ice ball upside-down atop the thermos. It takes 20 or so hours to freeze in my freezer.
Then you can simply add objects inside the ice ball mold. Make sure to shake them to get any air bubbles out and fill them to the top.
To make this lime spiral, I used this little tool called the Chef'n Lemon-Aid Citrus Spiralizer. I was trying it out and couldn't think of what to do with the spiralized lime once I'd made it. So I popped it into my ice ball mold, froze it overnight, and BEHOLD!
So, that came out pretty awesome.