Let's start with the basic question: Did you see significant growth? Did turbidity increase?

And why add lactose?

I added lactose as inducer for cellulase production and the solution turned from clear when cultivated to semi-turbid with some mass in the bottom.

it was in shaking incubator at 37C.

Your proposed fermentation medium (1% CMC, 0.25 gm K2HPO4, 0.125 gm KH2PO4, MgSO4.7H2O 0.05, NaCl 0.125 gm, CaCl2.2H2O 0.005 gm, FeSO4 0.0025 gm, 1gm Lactose in 250 ml) is a step towards a defined medium, but it likely lacks a sufficient nitrogen source and other essential nutrients for optimal and robust growth of Bacillus subtilis. While it contains a carbon source (lactose and CMC) and several mineral salts which act as a buffer and provide some essential ions, B. subtilis is a heterotrophic bacterium that requires a complete suite of nutrients for significant biomass production.

To achieve effective cellulase production, you first need to ensure strong bacterial growth. A simple solution of lactose (or CMC) in water, even with the included buffer and some salts, is generally insufficient for optimal B. subtilis proliferation.

Here's a more scientific approach to developing your fermentation medium:

For a strong starting point on a defined medium for Bacillus subtilis growth, I highly recommend referring to the following paper:

Monteiro, S., Clemente, J., Carrondo, M. and Cunha, A. (2014) Enhanced Spore Production of Bacillus subtilis Grown in a Chemically Defined Medium. Advances in Microbiology, 4, 444-454. doi: 10.4236/aim.2014.48049.

This paper provides a detailed formulation for a chemically defined medium that supports excellent B. subtilis growth, which you can then adapt by adding your inducing agents like CMC. Cheers!