NavList:

The time of LAN is not at all critical. In most latitudes, the change in altitude is not noticeable for anywhere from three to eight minutes around noon. Try it yourself. You can check with actual observations, or you can simulate local noon in software like Stellarium or using (the free on Android, inexpensive on iPhone/iPad version of) my "GPS Anti Spoof" app. Note that if your latitude matches the Sun's declination within a couple of degrees, the "hang time" at local noon is very brief, and then there are other tricks that can help.

Also note that this implies that all the noise about predicting and calculating the time of LAN in many textbooks on celestial navigation is wasted effort. Noon is an observable event. Youu watch and wait for the altitude to stop changing. That's noon. 

Frank Reed