  Elliptic soliton solutions, i.e., a hierarchy of functions based on an
elliptic seed solution, are constructed using an elliptic Cauchy kernel, for
integrable lattice equations of Kadomtsev-Petviashvili (KP) type. This
comprises the lattice KP, modified KP (mKP) and Schwarzian KP (SKP) equations
as well as Hirota's bilinear KP equation, and their successive continuum
limits. The reduction to the elliptic soliton solutions of KdV type lattice
equations is also discussed.
