In doing my own tests with this (using that same formula), the lerp causes the door to lag behind the image point on the player when the player is moving, even if the lerp amount is large.
I even tried to change it up so that all the calculations for door movement were "local" and relative to player space, rather than targeting the player image points in world space. It was a little better, but still laggy.
I'm sure there is a formula out there that will do this perfectly, and I am also sure that formula is way out of range of my math skills. So as I mentioned before, I think the simplest and most accurate method would be to make door opening and door closing animations for your door sprite.
(If Construct had any sort of parenting ability, you could parent the player to the door and move the door child locally along it's own Y axis relative to the player. All other positioning and rotation of the player parent would be automatically transferred to the door. Unfortunately, Construct doesn't do that... so, uh, this is a moot point I guess )