Logo is a Lisp and yet does not really use s-expressions, and even has infix operators.
Now, you might argue that means Logo is not a Lisp, but it is actually extremely similar to basic Scheme. You could turn an interpreter for one into an interpreter for the other with mostly minor tweaks. It's also a dialect of Lisp historically.
Qi uses S-Expressions but it's got strong typing, pattern matching, and optional lazy evaluation. Sounds a lot more like Haskell than Scheme to me.
I'm not sure there is such a thing as a "Lisp." If you mean S-expression language, just say s-expression language. Wedging in Lisp as a substitute conflates the issue.
How about: If you program in it using s-expressions, it’s a Lisp.