The current study is fully devoted to studying differential subordination and superordination theorems of analytic functions with some sandwich results involving linear operators Iλs,a,μ. This operator was obtained by the Hadamard product with the family of integral operators and the Hurwitlz-Lerch Zeta function. The current results demonstrate the possibility and capability of extracting the Sandwich theorem, and the conclusion includes differential subordination and differential superordination.