We present \lcsym, a typed $\lambda$-calculus for \emph{lenient symbolic execution}, where some language constructs do not recognize symbolic values. Its type system, however, ensures safe behavior of all symbolic values in a program. Our calculus extends a base occurrence typing system with symbolic types and mutable state, making it a suitable model for both functional and imperative symbolically executed languages. Naively allowing mutation in this mixed setting introduces soundness issues, however, so we further add \emph{concreteness polymorphism}, which restores soundness without rejecting too many valid programs. To show that our calculus is a useful model for a real language, we implemented Typed Rosette, a typed extension of the solver-aided Rosette language. We evaluate Typed Rosette by porting a large code base, demonstrating that our type system accommodates a wide variety of symbolically executed programs.