Disclaimer: I teach classes at the college level.
I think the situation is more vague than you make it appear. A teacher is hired to teach students, often with the understanding that they have prior experience teaching this class (and that includes lesson plans).
One the one hand you can argue that a lesson plan is an integral part of the "teaching" activity. On the other, you can argue that teachers develops it on their own to aid their teaching.
Often, this lesson plan was developed prior to their current job (these have a tendency to develop over the lifetime of the teacher and are some are passed from one generation to the next)
Mostly, a lesson plan is an external representation of internalized knowledge and organization of the subject matter.
Would you argue that the teacher's knowledge of math also belongs to the school if they teach math?
To use the programmer analogy that has been floating around this discussion, if a programmer learned prolog as part of her current job is she allowed to utilize her newly acquired knowledge in her next job?
Can she tutor other programmers in prolog?
A lesson plan is just that - a form of knowledge preservation. It helps the teacher remember how they taught the class before so they can more easily teach it again and become better over time.
I am not a lawyer, so I cannot claim to answer whether a lesson plan created by a teacher is a "work for hire", but my intuition is that the consensus among teachers is that it belongs to the teacher.
In any case, I do not think the situation is as clear cut as you make it to be, especially if we consider how lesson plans come to be and how they are used.