Rotation Around Tilted Y-Axis

I have an object that is tilted back 15 degrees.
I want to be able to rotate it X degrees around the tilted Y-axis with a LERP, like so:

transform.localRotation = Quaternion.Lerp(transform.localRotation, TARGET_ROTATION, Time.fixedDeltaTime * 0.75f);

This works for an object is not tilted but, with my tilted object, it obviously, doesn’t.
My problem is getting the proper TARGET_ROTATION quaternion.

I have beat my head against the wall on this for hours.
I would appreciate any help.
– Paul

Well, Lerp wouldn’t generally work too well for something like this. I’d probably go with a simpler solution:

float rotAroundAxis;
Quaternion axisTilt;
transform.localRotation = Quaternion.Euler(0, rotAroundAxis, 0) * axisTilt;

Then you set up the axisTilt variable to be the rotation quaternion of just the tilt in Start(), and update the rotAroundAxis variable each frame.