A two-dimensional (2D) two-component and two-phase lattice Boltzmann method (LBM) with large density ratio is developed based on a modified Shan-Chen pseudopotential model combined with the deferent time step method. The present LBM model can simulate the gas-liquid two-phase flow with density ratio up to around 800. To validate the model, the pressure difference between the inside and outside of a bubble varying with its radius is simulated with different gas-liquid interact parameters and density ratios. The results are found to obey the Laplace law. Then, the LBM is coupled with the cellular automaton (CA) method used for simulating the solid phase growth, and the finite difference method (FDM) used for calculating the temperature field. The LBM-CA-FDM coupled model is used to simulate the interaction between bubble and the solidification interface. The results show that the existence of adiabatic bubble influences the distribution of temperature field in front of solidification interface, which leads to a bulge of the solid-liquid interface when it is close to the bubble. Under the conditions of different growth rates, the bubble is either engulfed or pushed away by the growing solid-liquid interface. The simulation results agree reasonably well with those observed experimentally.