Lattice Boltzmann equations with dependence on a parameter are proposed. The construction of finite-difference schemes is based on the integral form of the system of kinetic equations with discrete velocities. The schemes are developed with usage of quadrature formulas. It is demonstrated, that at some parameter values the second order of approximation takes place. The stability conditions are obtained. The possibilities of application to fluid dynamics problems are demonstrated on the solutions of 2D lid-driven cavity flow problem and problem of the flow in channel with rectangular stricture. Obtained results are compared with the results obtained by other numerical methods.