To address your last point (albeit late): whether the lookup table is stored in RAM or ROM makes no difference to the size needed (although it would almost never make sense to store a multiplication table like this in RAM).
If it were stored in RAM you would either have to load it from ROM or populate it manually, neither of which make much sense in the typical situations where you might use a lookup-table.
Copying a ROM table to RAM would typically only be used if the contents were to be updated over time, and the ROM copy is just the starting point (not the case with multiplication). The only other likely use-case that comes to mind would be where you use a ROM to "bootstrap" the system -- copying programs and data to RAM -- and then switch the ROM out of normal address-space and run everything from RAM.
As for populating manually: using a look-up table for multiplication would tend to imply that you're on fairly low-level hardware, where you either don't have a full-blown CPU (in which case there would be nothing to populate the table) or it's a fairly basic CPU (in which multiplication is slow). In the latter case, it could make sense to populate a RAM table at start-up (essentially creating a cache), but since you would have to evaluate all combinations, this would lead to a lengthy delay before you could do "real work".