I have shot lino bullets in the 223 and 22 K-Hornet at 3,000 fps. As Jim said the accuracy is not as good as around 2,300 to 2,700 fps, depending on powder and cartridge.
The 22 K-Hornet does better at 2,700 fps than the 223. I think it might be the amount of powder needed to get equal velocities or the 3" longer barrel on the 223.
Lino shoots much better than bullets that are water dropped or heat treated to try to get equal hardness.