Be grateful the lies are about petty issues, but keep a careful eye out. My guess is he's territorial, and maybe fussy like that at home, and thinks people moved his reading glasses and ate the last piece of pie.
We had one who lied about grave matters so we had no choice but to leave. I would be careful not to jump the gun if it's a matter of your kids not getting traditional Religion classes. If the religion teachers are good, I would make every effort to tolerate the annoyance you described and somehow make the principal feel more happy about sharing the space.