"Fallen nature" is nothing but a "Theological LIE" created by "Theologians" for their own religious purposes!!! Man's NATURE never changed. Adam had a HUMAN NATURE that NEVER CHANGED, and so did Jesus, you, and me!!!!
Since Jesus was TEMPTED IN EVERY RESPECT AS WE ARE, then obviously HE had LUSTS and STRONG PERSONAL DESIRES just like Adam, and us.
The difference is that JESUS, while being TEMPTED like us, never let HIS LUST CONCEIVE and become SINFUL ACTIONS. (James 1:14,15)