In the case of elk, the same way as you would use any ground red meat. It is lower in fat so may need some help in that department. @KennethT often cooks with elk, so you may want to look at some of his posts.
In fact, in many cultures, lamb and goat are not differentiated, at all. Use it the same as ground lamb. Goat can be gamier but that depends largely on how it was raised. - often they are indistinguishable.
Of course, both these proteins have dedicated topics already which you could have consulted.
