What are the advantages and disadvantages of using LISP for constraint satisfaction in 3D space We are currently working on developing a 3D modeling software that allows designers to set spatial constraints to models. The computer then should generate a 3D mesh conforming to these constraints.

Why should or shouldn't we use Lisp for the constraint satisfaction part? Will Prolog environment be any better? Or should we stick to C/C++ libraries?

One requirement we have is that we want to use the Unity Game Engine as it has a lot of 3D tools built in
This is actually a question which will only receive opinion based answer's. A question you should ask yourself is if the constraint part is really that complex that it is worth to use a different programming language. Unity itself offers a C# API [1] and I would therefore stick with that.

[1] https://unity3d.com/programming-in-unity