Surface x-ray scattering has been used to study in-situ the structure of Pb monolayers electrochemically adsorbed on Ag (111) electrodes. Pb forms an incommensurate, hexagonal two-dimensional (2D) solid, which is rotated approximately 4.5° from the substrate symmetry directions and compressed relative to bulk Pb. Between monolayer formation and bulk deposition, the Pb-Pb near neighbor distance decreases linearly with applied potential. Due to the chemical equilibrium between the Pb monolayer and the Pb in solution, the isothermal compressibility of the monolayer can be measured and is in good agreement with that calculated for a 2D non-interacting free electron gas model of the monolayer. It is observed that the intensity of surface diffraction from the Ag substrate (the Ag crystal truncation rod) decreases when the Pb monolayer is adsorbed, although the cause of this is not known.