Generally, no they don't lay when they are moulting but some people's birds do. Mine never have.
The CL should only lay blue, right? I can see some variation in the color of my EE's eggs. Of my original 2 one (the one that was eaten by a fox April 2014) layed blue the other green. But sometimes the blue egg was shading kinda toward green and sometimes the green shaded somewhat toward blue and I really had to look at them together to see which was which.
Same with the three 2015 chicks. One is green, one blue, one in between. I can tell the blue from the green but sometimes the "in between" looks blue and sometimes green until I compare it to the other two.
My understanding is that a truly blue egg is a white shell impregnated all the way through with blue and a green egg, having a brown component would be the same but maybe like brown layers, the hen coats some brown "paint" on the outside of the egg as it nears the shipping dock? Thus the green color "changes" depending on how much "paint" was applied. Thinner and more of the blue will show through resulting in a lighter green. Heavier and less of the blue shows through resulting in a darker green.