The LGO by itself is meant to be a combination of an MBA with technical expertise at a higher level. Harvard offers dual degrees with certain other Harvard schools. And it lets you cross register at MIT for your second year MBA elective courses, for upto two courses, if I am not mistaken.
However, I don't think there's a dual program established between HBS and MIT yet. Assuming your technical pursuit lays in MIT, maybe you can try to figure out what specific field interests you and contact a professor there and see if something is possible on a special case-by-case basis.
I am not sure how much this helps, and I would love to have some others' input on this as well!