鞍 isn't a typo here. The situation is quite similar to jousting, so I think it's safe to say only riders use the 竜槍.
I thought masu-stem could be used to list out one of several options in the case of generalizations, but it seems I was mistaken.
But I still can't understand the reasoning of why they would go through the trouble of holding the lance under their arms, and then suddenly fix it on, when they can fix it on from the very beginning. They don't move, nor are there signs of any actions being performed between 'holding it under their arms' and fixing it onto the saddle ring, so what's the point of even holding it under the arm? It just seems easier skip the first step, or only do one of the actions.
Well, that was probably most confused me about the sentence. Thanks a lot for clarifying Toritoribe.