Abstract: In this paper, the lattice Boltzmann method is utilised to solve a class of fractional order diffusion equations in asymmetric Riemann-Liouville spaces. The initial procedure entails the pre-processing of fractional order derivatives, which is achieved through the utilisation of linear interpolation and the integral median theorem. This process facilitates the conversion of fractional order equations into integer order equations. The establishment of the lattice Boltzmann model with second-order accuracy is achieved through the implementation of the Chapman-Enskog multiscale expansion technique, with the equilibrium state distribution function being selected in a manner that is deemed appropriate. The validity of the proposed model is finally verified by numerical experimentation, with the numerical results of the model under different weights and fractional orders demonstrating good agreement with the exact solution.