Comment by flohofwoe

On the Z80 any memory access had a fixed cost of 3 clock cycles (in reality the memory system could inject wait cycles, but that was an esoteric case). Together with the instruction fetch of 4 clock cycles the fastest instruction to load an 8-bit value from an address that's already in a 16-bit register (like LD A,(HL)) takes 7 clock cycles.

The fastest instructions that didn't access memory (like adding two 8-bit registers) were 4 clock cycles, so there's really not much room to beat a memory access with computation.

Today "it depends", I still use lookup tables in some places in my home computer emulators, but only after benchmarking showed that the table is actually slightly faster.