I am not exactly sure if this is what you wanted me to try but here is my trial from interpreter--
>>> from sympy.core.cache import cacheit
>>> from sympy import Lambda, var
>>> def func(L):
...     return L(1)
... 
>>> var('variable_1')
variable_1
>>> func(Lambda(x, x + variable_1))
variable_1 + 1
>>> func(Lambda(x, 2*x))
2
>>> func(Lambda(x, x/variable_1))
1/variable_1
>>> func(Lambda(x, variable_1/x))
variable_1
>>> func(Lambda(x, x + variable_1)