As the particle lateral density distribution of extensive air showers (EAS) is the key quantity for most of the ground-based cosmic-ray experiments, the lateral distribution function (LDF) of EAS plays an important role in the analysis of the air-shower events. It can be used to derive air-shower size and age, etc, which, in turn, can be used to estimate the energy and particle type of the incident primary cosmic rays. To measure the chemical compositions of primary cosmic rays at the knee energies, the Tibet AS$\gamma$ collaboration started constructing a new hybrid detector system in Tibet, China, in 2014. The new hybrid experiment consists of the air-shower array (Tibet-AS), the air-shower core-detector array (YAC) and the underground water-Cherenkov muon-detector array (MD). Based on a full Monte-Carlo simulation for the new Tibet hybrid experiment (Tibet-AS+YAC+MD), we developed modified LDFs for proton-induced and iron-induced air showers, respectively. As an application of the new LDFs, we derive some characteristic parameters sensitive to the primary composition.