In mpmath as shipped currently with sympy (i.e. 0.17):
In [1]: mpmath.lerchphi(1.0000000, 4.1+1j, 1.0)
Out[1]: (nan + nanj)
In [2]: mpmath.lerchphi(1.00000001, 4.1+1j, 1.0)
Out[2]: (1.04978614989967 - 0.0531909196466606j)
In [3]: mpmath.zeta(4.1+1j, 1.0)
Out[3]: (1.04978614939285 - 0.0531909188369103j)
The first is the problem, the second shows that the evaluation bug seems to be confined to z exactly unity. Since lerchphi reduces to hurwitz zeta for z=1, the third is the desired output.
Original issue for #251: http://code.google.com/p/mpmath/issues/detail?id=211
Original author: https://code.google.com/u/104531927090589914088/