I had the thought, last evening while thinking over your questions and the various posts, that the LBH was what the post 1940 Army calls “A Meeting Engagement.” That is where two forces, knowing that someone is somewhere in front of them find and engage each other, without a formal plan of battle/attack. Thus the elements utilize the tactics they have found successful in the past.
The “most famous” [IMO] meeting engagement before this, on American soil, was the first day of the Battle of Gettysburg.
I spent 2 years as the S-2 of an armored cavalry squadron in the Fulda Gap (1983-85). We had our defensive battle plans for along the East-West German border, if we had time to get there, but otherwise, we had to rely on our training to fight a meeting engagement if the Soviets crossed the border before the V Corps forces were in position, i.e. a “no warning war scenario.” And during my time as a field artillery forward observer with a 3d Armored Division tank company (I had my own M-60A2 tank to work from) 75-78.
The Sioux were not laying in wait for ambush?