We present four new epochs of Ks-band images of the young pre-transitional disk around LkCa 15, and perform extensive forward modeling to derive the physical parameters of the disk. We find indications of strongly anisotropic scattering (Henyey-Greenstein g = 0.67 [-0.11,+0.18]) and a significantly tapered gap edge (round wall), but see no evidence that the inner disk, whose existence is predicted by the spectral energy distribution, shadows the outer regions of the disk visible in our images. We marginally confirm the existence of an offset between the disk center and the star along the line of nodes; however, the magnitude of this offset (x = 27 [-20,+19] mas) is notably lower than that found in our earlier H-band images (Thalmann et al. 2010). Intriguingly, we also find, at high significance, an offset of y = 69 [-25, +49] mas perpendicular to the line of nodes. If confirmed by future observations, this would imply a highly elliptical -- or otherwise asymmetric -- disk gap with an effective eccentricity of e = ~0.3. Such asymmetry would most likely be the result of dynamical sculpting by one or more unseen planets in the system. Finally, we find that the bright arc of scattered light we see in direct imaging observations originates from the near side of the disk, and appears brighter than the far side because of strong forward scattering.