Agreed, it comes from the .50. BUT it has now morphed into a standard US Army command for all weapons.
It now generally means "make sure it's on safe and then chamber a round"- that shouldn't make sense with an M16- BUT the US Army drill is to ALWAYS have the weapon cocked and on safe, even with no magazine fitted. In this way the weapon should always be on safe and there is never confusion about whether or not a round is in the chamber- it doesn't matter- it should always be on safe. So "lock and load" is used, as is "lock and unload" meaning the same thing "make sure it's on safe if you were just firing, then unload and prove clear, then place it on safe" the EASE SPRINGS is not done as part of their drill.