We study the effect of hydrophobically modified polymers (hm-polymers) on the phase behavior and membrane elastic properties of the lyotropic lamellar (L-alpha) phase of the nonionic surfactant penta(ethylene glycol) dodecyl ether (C12E5). The hm-polymer is a model comb-graft polymer with monodisperse PEG blocks (loops) of 6, 12, or 35 kg/mol connecting C-18 stearylamide hydrophobes. The polymer is of interest because both its loops and hydrophobes are biocompatible. The membrane properties are extracted from the small-angle neutron scattering data based on the model of Nallet et al. The monophasic L-alpha region exists over a narrower membrane volume fraction range but to a higher polymer concentration for hmPEGs with larger PEG spacers. The rigidity of the membranes increases by 40% with decreasing PEG spacer size from 12 to 6 kg/mol or increasing polymer concentration. For hmPEG polymers with 2-3 loops, the effect of finite chain lengths plays a role on the phase behavior and membrane properties.