We probe in two different ways the competing attractive and repulsive forces that create lamellar arrays of the phospholipid lecithin when in equilibrium with pure water. The first probe involves the addition of low molecular weight solutes, glucose and sucrose, to a system where the phospholipid is immersed in a large excess of water. Small solutes can enter the aqueous region between bilayers. Their effect is first to increase and then to decrease the separation between bilayers as sugar concentration increases. We interpret this waxing and waning of the lattice spacing in terms of the successive weakening and strengthening of the attractive van der Waals forces originally responsible for creation of a stable lattice. The second probe is an "osmotic stress method," in which very high molecular weight neutral polymer is added to the pure water phase but is unable to enter the multilayers. The polymer competes for water with the lamellar lattice, and thereby compresses it. From the resulting spacing (determined by X-ray diffraction) and the directly measured osmotic pressure, we find a force vs. distance curve for compressing the lattice (or, equivalently, the free energy of transfer to bulk water of water between bilayers. This method reveals a very strong, exponentially varying "hydration force" with a decay distance of about 2 A.