Ok, I was thinking about two stationary points, with the 0-1 value being used to move, which is how I usually use lerp(). What wasn't made clear was that "here.x" is actually the sprite's own x. You should have said set "set .x to lerp(.x,there.x,1-0.5^timedelta)".
For this kind of movement like you want, I usually just do
set .x to .x+(abs(there.x-.x)/(somevalue*timedelta)).