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This paper studies the optimised Lambertian order (OLO) of light-emitting diodes (LEDs) for an indoor non-directed line of sight optical wireless communication (NLOS-OWC) systems. We firstly derive an expression of the OLO from a conventional Lambertian LED model, Then, we analyse the indoor multi-cell NLOS-OWC channel characteristics including optical power distribution and multipath time dispersion for two cases of one-cell and four-cell configurations. Furthermore, we estimate the transmission bandwidth by simulating the channel frequency response. Numerical results show that, by using OLO a significant improvement of the transmission bandwidth can be achieved for in indoor NLOS-OWC systems, in particular, for multi-cell configurations.