Your screen cap is a control for light ink to dark ink in cyan. This is a control applied before, during, or right after linearization.
Controlling K as I mention in #2 is done within the controls for the ICC its self. It will usually be shared with controls for Total Ink (0-400), GCR, UCR, and maybe black "width".
What you're looking to effect with the K start is when the K ink starts to get used in the lightness scale. As far as I know, most profiling software makes this number relative to the use of cyan. IOW, when does K start to be used relative to the amount of cyan. So if you set your K start to 20, that means once there is 20% cyan use, the K dot will start to be mixed in. I think it's easier to just think of it in terms of when K starts to get used in the lightness scale.
Earlier (lower) values use K dots in lighter colors and start to apply your GCR sooner. Later (higher) values do not use K dots until the colors get darker. Using K in light colors makes for some grainy looking prints because your eye resolves the contrast of the K dot against the light color easily. Lay people will describe this as looking grainy or low rez. Supressing the K dot until the colors are darker helps hide the contrasty dot and depends on your CMY and lc lm if you have them to mix colors from. This makes for a smoother, "higher rez" looking print, especially if you have lc lm.
Hope this helps. When in doubt, go with 45 for a K start for solvent inkjet and you'll be safe.