A 256x3=768-byte lookup table will almost certainly be faster on a CPU. It will fit easily in L1 cache, and can extract 3 bytes at a time.

Ironically, x86 has an instruction, XLATB, that does almost exactly this (looking up a byte in a 256-byte table) -- but using it is actually slower than using an equivalent MOVZX RAX,AL; MOV AL,[RBX+RAX] sequence on modern CPUs.