An LSA won't have a standard category airworthiness certificate, so can't be operated internationally on the N reg without specific permission of a foreign state (normally only granted for short periods). It also won't qualify for a standard Cof A in any other country.
So it will only be permitted if it conforms to the type certificate of a standard certified aircraft or is eligible for a permit to fly (possible for some amateur built types like the RV-12).
Do you have a type in mind?
If so, you may get a more specific answer.
[Edit. Just noticed that you're in Oz, so you will need to contact your own authority to see whether it qualifies for any kind of airworthiness approval).