In my opinion, there isn't a real LBM model  of radiation transfer equation at present. they are fake LBM model to solve radiative heat transfer. 

By the way , The grid in LBM and FVM or FDM has the little same. Different LBM model such D1Q2 or D1Q3 have different gird depend on LBM model you choose.however ,grid in FVM and FDM can be changed if you like .

you may want to check this:

http://www.sciencedirect.com/science/article/pii/S0017931015308954