Lisp is used for AI because it supports the implementation of software that computes with symbols very well. Symbols, symbolic expressions and computing with those is at the core of Lisp.
Typical AI areas for computing with symbols were/are: computer algebra, theorem proving, planning systems, diagnosis, rewrite systems, knowledge representation and reasoning, logic languages, machine translation, expert systems, and more.
It is then no surprise that many famous AI applications in these domains were written in Lisp:
- Macsyma as the first large computer algebra system.
- ACL2 as a widely used theorem prover, for example used by AMD.
- DART as the logistics planner used during the first Gulf war by the US military. This Lisp application alone is said to have paid back for all US investments in AI research at that time.
- SPIKE, the planning and scheduling application for the Hubble Space Telescope. Also used by several other large telescopes.
- CYC, one of the largest software systems written. Representation and reasoning in the domain of human common sense knowledge.
- METAL, one of the first commercially used natural language translation systems.
- American Express' Authorizer's Assistant, which checks credit card transactions.
There are thousands of applications in these areas that are written in Lisp. Very common for those is that they need special capabilities in the area of symbolic processing. One implements special languages that have special interpreters/compilers in these domains on top of Lisp. Lisp allows one to create representations for symbolic data and programs and can implement all kinds of machinery to manipulate these expressions (math formulas, logic formulas, plans, ...).
(Note that lots of other general purpose programming languages are used in AI, too. I have tried to answer why especially Lisp is used in AI.)