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I think you are confused about what "lean burn" means. If you are talking about the engine cutting fuel when you are off the go pedal, that's "deceleration fuel cut off" or DFCO as it is called on this forum often. Lean burn is a function of.. i think only Honda engines where you are cruising at highway speed and it starts to run a lean fuel mixture (less than the usual fuel/air ratio).
If you are going to have to use your brakes, then coast in gear. If you are able to pop it into neutral, coast a while, then get back into drive to continue on - go that route. So on a hill, you could put it in N, then when your speed gets a little too high, put it in D, if that slows you down too much, put it back in N. The brake pedal is the enemy.
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