Permatec, Ultra Slick, Extreme Sport, Synthetic grease. 85g tube. My local auto parts guy who was in the industry for decades as a mechanic recommended this for as close a replacement as he knew in his store to duplicate what lubriplate was required for.
Lots of good greases as mentioned above remember it ain't turning 1000 rpm with a 3 ton load applied all the time, the only issue I could see in the way we use our rifles normally is extreme cold properties, say sub -20C. I'm not sure if lubriplate was figured into the late 50's grease requirements for an "All weather, All conditions" grease based partly on its good properties down really low for a grease in it's day circa 1955.
I'm assuming a light application would suffice?