The lyman that I used to have that took those dies was a Tru-line Jr turret press. It took 9/16" fine threaded die all black as HiBC stated. I'm trying to upload a picture so if it doesn't so up bear with me. The die beside the black ones is a standard 7/8" die.
Notice the lyman box the dies came out of reads Lyman Gun Site Co. these dies were my fathers from the 1940's