In fact, in lerp(x,y,z) the z stands for the time that it will lerp from x to y.
You choosed dt as z-factor, wich is fine, but liniair.
The thing is, if you change z to a function, also the time is effected. It wil be a bit try and error. (for me it will be).
So if you change z to 'dt^n' with n a number your choose, you will have a curve. How bigger you choose n to be, how steeper the curve.
You can google on "graph for x^3" to see the curve drawn. Or x^4 ... any math.
But now you also changed the time. So you have to correct it somewhat to youre liking.
That is why i proposed (dt^n)/m, where m is any number that gives you an acceptable time.
So, you choose n and m and it wil be, with by instance n = 3 and m = 2 ... lerp(x,y,(dt^3)/2)