Cyclone III internal ROM(ram) speed

LUTs will probably be a slower. You can only do a 4:1 LUT in a ROM, so muxing them together to build a 256 deep table will be slow. How fast can the memory run? Put in timing constraints and Quartus will tell you. But note that only giving it one clock cycle means the read address registers will be used. You'll then have the access of time of the memory to deal with. I don't know what that is, but let's say it's 4ns. If you could register the output of the ROM, then you'd make 200MHz easily. But without it being registered that means you have something after the ROM, whether it be combinatorial logic, output ports, etc. before it is finally registered again. All of that is going to cut into how fast it runs. So it's not a question of just the ROM, but the ROM plus the rest of the path, which is up to you. (Which is what TimeQuest is for)

Besides asking timing analysis for an exact answer, you'll find "Memory Block Performance Specifications" in the device handbook for a first estimation. It suggests that 200 MHz isn't a problem for the RAM blocks as such. I guess that the specifications are assuming registered RAM outputs however.

Thank you for good answers