You could save the current modelview matrix for the first object using glGetFloatv, and use glLoadMatrix later to render the object that would be aligned with it. Or if they are drawn roughly at the same time, you could just use glPushMatrix and glPopMatrix. Push the matrix onto the stack where alignment should start, do other drawing and translation to finish first object, then pop the matrix off the stack to start drawing the second object.
That would work but I need the rotation of the current object at anytime after the model is created. The problem is that the original model is a set of lines and a more complex model is going to be placed in the same location. I’m believe the matrix or normalised vectors of the current models xyz axies can give the XYZ angles needed to glrotate the new model into position.