for those who still in in ios 6.0.2 or below 6.1.2. this is my method of updating the carrier list. tis method is only to make sure that itunes detect your iphone is 6.1.3 and after that itunes will automatic check the carrier setting. the method are:

1) use ifunbox and connect your iphone and go to.
Raw system file>Device>system>coreservices>systemversion.plist.
2)copy the systemversion.plist to your pc and open the file. and you should see the "<string>6.0.2</string>" in the plist. after that change into 6.1.2 or 6.1.3 and after that safe the file.
3) copy back into your iphone in the
Raw system file>Device>system>coreservices> and replace with the original systemversion.plist.
4)reboot your phone.
5) after that you go into system>general>about. check the system it is either 6.1.3 or not.
6) connect your iphone into itunes and itunes will detect and ask you to update the carrier setting.
7) update the carrier setting.
8) you should see the carrier setting is 14.1 in the general.
9) do the same method to change back the systemverion.plist to change into original 6.0.2. and reboot the phone.

your phone will detect the LTE.

p/s: some user may encounter automatic update when they check the phone is step 5.

goog luck.
Added:

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Using ifunbox to take the file out from iphone.

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ios 6.0.2 with LTE.
this method works on jailbroken iphone. as for none jailbroken iphone. you can always on latest firmware and should be no problem in updating the iphone carrier setting.