The “LC” headstamps are from Lake City Arsenal. The military designation for this cartridge was "Cartridge, Ball, M2. There were similar designations for AP, Tracer, Blank, Grenade Launching ctg., Incendiary, API, and dummy rounds. May have missed some loadings in there. I will leave it to the .30-06 experts to give designations for all of those, if wanted.
Some other designations one sees are “.30 Ball Model of 1906” and commercially, simply “.30-06” or ".30-06 Springfield.
Those cartridges you show in links were likely for the Browning Machineguns M1919A4 or M1919A6. Originally, the belts were of cloth, first white and later olive drab. The cloth belts were still being used in the 1950s, even though I believe the links came out in the latter part of WWII. I only know these rounds from being in a light weapons squad when I first went into the Army. I have never collected this caliber. On stripper clips or enbloc chargers, these cartridges were also used in the M1903, M1903A1, 03A3 and 03A4 Springfield bolt-action rifles, as well as the Browning M1918 Automatic rifle (in Magazines) and the M1 (Garand) Rifle. All were used in WWII.
There were other designations for aircraft machineguns of .30 caliber, but I am not familiar with them off the top of my head.