In the 7.62 NATO, I've mostly seen Lake City issued ammo for marksmanship teams and sniping over the years. The M118, M852 and M118LR have all been Lake City. The cases are headstamped with the LC initials.
In the 300 Winchester magnum it has mostly been Federal ammo with a 190 grain MK bullet. The cases have been headstamped with the FC logo.
In the 338 Lapua Magnum, the ammo that I've used had an "L" within a shield on the headstamp.
For ball ammo in the 5.56 (A1, the A2 and M4), 9mm and the 45, I've seen TZZ, FC, WCC and Lake City all issued.