Planewise dipole sums give the electric field at a point due to an array of electric dipole moments in a plane. Calculations are reported for model lattice structures of Langmuir-Blodgett films with elongated molecules represented by a string of spherical "beads" or submolecules; interactions are averaged over submolecules. Results are given for parent hexagonal and tetragonal lattices, with molecules allowed to tilt away from the vertical and with the in-layer cell parameters allowed to distort from equality. Beyond about five submolecules, molecular length makes little difference. Interactions within a layer dominate, with those between adjacent layers much smaller and those between remoter layers negligible. Tilt affects the interactions more than the detailed lattice structure does. The results provide a key ingredient for theories of the optical and electrical properties of Langmuir-Blodgett films.