As long as the polarization is the same, yes. D* and E* are both circular-polarized, as is Evu.
There's also the matter if the LNB's are "stacked" Dish-style or L/R CP like DirecTV. The stacked LNB's won't work with DirecTV unless a destacker is used, although I've never heard of them beign used for a home install.
There is no difference between SD and HD LNB's.