A proposal for simulating the Dicke-Lattice model in a mechanics-controlled hybrid quantum system is studied here. Where an array of coupled mechanical resonators (MRs) homogeneously interact with a group of trapped Bose-Einstein condensates (BECs) through the gradient magnetic field induced by the oscillating resonators. Assisted by the classical dichromatic radio-wave (RW) fields, each subsystem with a pair of BEC-MR interaction can mimic the Dicke type spin-phonon interaction, and the whole system is therefore extended to a lattice of Dicke models with an additional adjacent phonon-phonon hopping couplings. For this lattice model with the Z2 symmetry, its quantum phase transitions (QPTs) behavior can be controlled by this periodic phonon-phonon interaction in the momentum space. This investigation may be considered as a fresh attempt on manipulating the critical behavior of the collective spins through the external mechanics method.