Samsung Galzxy Note 3 comes with the following three versions:
Samsung Galaxy Note 3 N9000 - 3G connectivity
Samsung Galaxy Note 3 N9002 - dual SIM card support
Samsung Galaxy Note 3 N9005 - 3G & LTE connectivity
Now if you have N9000 or N9002 then you can not flash LTE on it, if you have N9005 then I don't see any issue with it.