The lateral distribution function (LDF) for coherent electromagnetic radiation from air showers initiated by ultra-high-energy cosmic rays is calculated using a macroscopic description. A new expression is derived to calculate the coherent radio pulse at small distances from the observer. It is shown that for small distances to the shower axis the shape of the electric pulse is determined by the 'pancake' function, describing the longitudinal distribution of charged particles within the shower front, while for large distances the pulse is determined by the shower profile. This reflects in a different scaling of the LDF at small and at large distances. As a first application we calculate the LDF for proton- and iron-induced showers and we show that this offers a very sensitive measure to discriminate between these two. We show that due to interference between the geo-magnetic and the charge-excess contributions the intensity pattern of the radiation is not circular symmetric.