Lattice thermal conductivity in Cu-Al alloys is calculated for the first time within a two-dimensional formalism involving the scattering of phonons by strain fields of finite spatial extent around randomly oriented dislocations of edge and screw character. For the finite strain fields, scattering widths indicate that long-wavelength phonons scatter very weakly. In addition to phonon scattering by the strain field around the dislocation, phonon-electron scattering is included to obtain the overall phonon relaxation rate. Comparison is made between the calculated results and measurements on the commercial alloy Evanohm. Evanohm has a very high residual resistivity and thus possesses a low electronic thermal conductivity. Therefore, the phonon contribution to the thermal conductivity may be unambiguously identified for this alloy unlike the situation encountered for most other alloys at very low temperatures. The calculated lattice thermal conductivity is found to depart from the usual ${T}^{2}$ dependence in general agreement with the measurements on Evanohm.