The LDL remains off during LF's because of appearance. It wouldn't look right jumping from the local boxes to the national feed with the LDL suddenly on screen.
About Dish's LDL... IIRC both DirecTV and Dish are controlled via the same config file (seprate systems, but similar configuration) so when TWC removed the LDL from showing during the LF's for DirecTV, it problaly got applied to Dish's LDL as well.