Does Format Preserving Encryption have significant advantages over a randomly generated lookup table?
any other considerations?


Yes.


In many common use cases the mapping table needs to be retained. That map changes each time a number is added; that's a backup / continuity of service headache.
The map is security-sensitive: it contains all the clear phone numbers, and information which (combined with other information) allows getting back to users.
The map can be large (at least about twice as large as the numbers themselves); that's a (perhaps minor) storage issue.
When the table grows large, there will be collisions in the mapping table, that's a special case which must be handled, and tested.
Timing attack on the map search code has the potential to leak information (that's also true of some FPE implementations, but proper FPE is less likely to leak something meaningful; in particular FPE won't leak if the creation of the entry was recent, which can happen with a map).
FPE's performance is predictable, when some map implementation have no specified worst-case performance.
FPE allows efficient implementation of direct and reverse map, when not all map implementations allow that.


Bottom line: encryption is desirable there. FPE is useful only if size or interoperability is a concern.