So why is understanding and visualizing your lift vector important? Because you roll your lift vector to where you want to go when you turn. To turn under the nose of your enemy (to avoid a shot or force an overshoot) you roll your lift vector under the enemy and pull to make your turn. When you think of turning in terms of lift vector placement, it simplifies maneuvers and makes them applicable in a variety of geometries.
I believe something was mentioned in this discussion that to avoid a shot or force an overshoot you "make a nose low turn". However, this statement is not entirely accurate. You can pass under the nose of your enemy (avoiding a shot and/or forcing an overshoot) while making a nose-high turn, provided your lift vector is still under your opponent. The geometry of the fight matters. For example, in a vertical scissors where you are both climbing (nose up), you can can still roll your lift vector under your opponent to turn under their nose and still be in a nose-up attitude. In fact, this can be advantageous -- by being nose-up you are decelerating. If your opponent pushes his nose down to force the crossing shot, the speed differential may force an overshoot and a possible reversal.
Correct lift vector placement is a simple but widely applicable concept. Most turn-fights are largely about lift vector placement and E-management. If you understand and think in those two terms, everything can become easier. That is why trainers tend to talk in simplified terms, like lift vector, instead of focusing on a set "maneuvers" (i.e. nose low turn) -- this is not to be "technical", but quite the opposite: to simplify things.
When I was less experienced, I used to think of most fights as being about maintaining speed and using the right maneuvers. Now I tend to think of many fights as maintaining the right lift vector placement and using the right speed.
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