What does LNAV engagement exactly mean? I notice the term LNAV engagement being frequently mentioned in aviation related discussions or in several FAA's relevant material. Take, for example, this quote from Order 8260.58A (PBN Instrument Procedure Design) which states:


  Order 8260.58A [5-1]: The ICA must be long enough to allow LNAV engagement (500 feet above airport elevation).


I am aware that LNAV means "Lateral NAVigation" but I have some trouble understanding what does "engagement" exactly mean and why an aircraft have to climb at 500 feet above airport's elevation before the initial turn for this engagement to happen. Could someone point me in the right direction?
Some old aircraft (737 Classic comes to mind) don't allow arming LNAV/NAV AFDS mode on the ground, as you normally have to be at least 400ft above ground (ICAO PANS OPS says 396ft) before making turns more than 15 degrees, at which point you would engage LNAV. I guess the regulation takes old aircraft into account.

On the newer aircraft, you can arm LNAV/NAV mode on the ground already and it normally becomes active at 50ft.