We present our implementation of lens-free video microscopy setup for the monitoring of adherent cell cultures. We use a multi-wavelength LED illumination together with a dedicated holographic reconstruction algorithm that allows for an efficient removal of twin images from the reconstructed phase image for densities up to those of confluent cell cultures (>500 cells/mm2). We thereby demonstrate that lens-free video microscopy, with a large field of view (~30 mm2) can enable us to capture the images of thousands of cells simultaneously and directly inside the incubator. It is then possible to trace and quantify single cells along several cell cycles. We thus prove that lens-free microscopy is a quantitative phase imaging technique enabling estimation of several metrics at the single cell level as a function of time, for example the area, dry mass, maximum thickness, major axis length and aspect ratio of each cell. Combined with cell tracking, it is then possible to extract important parameters such as the initial cell dry mass (just after cell division), the final cell dry mass (just before cell division), the average cell growth rate, and the cell cycle duration. As an example, we discuss the monitoring of a HeLa cell cultures which provided us with a data-set featuring more than 10 000 cell cycle tracks and more than 2x106 cell morphological measurements in a single time-lapse.