Lorenz-Mie multiple-scattering theory is used to perform semi-analytical calculations of the lossy dispersion relations of propagating modes in infinite chains of metallic spheres. Lossy modes are described by allowing the projection of the wavevector along the chain axis to be a complex number rather than the more common complex frequency description. We show that even when the constituent particles are much smaller than the wavelength, one generally needs to go well beyond the coupled dipole approximation to achieve stable predictions.