The way I achieve this is by using Cubic(a, b, c, d, x) instead of Lerp(a, b, x). Just set "a" and "b" in Cubic to what you set "a" to in Lerp and "c" and "d" to what you set "b" to and you should get the smooth movement you want. So basically:
Cubic(a, a, b, b, x).
I hope I explained that well enough.