That’s very tight for a transfer. Delays of up to an hour on departure or arrival of a flight to Narita are quite routine - especially if it’s a long haul flight. If you’re catching two different airlines, you’ll need to collect your luggage, go through immigration and customs, transfer to Terminal 3 (takes about 20 minutes) check-in again, go through immigration again and then go to your gate. It might be possible to go straight to Terminal 3 without going through immigration if you only have carry-on luggage, but you’ll need to check with the Low Cost Carrier to see if it’s possible. A lot of these airlines have really restricted service offerings and they aren’t very flexible - that’s why they’re cheap. Try contacting the airline directly and see what they say. If you have luggage though, there’s nothing you can do. Even transferring within the airport in an hour is really pushing it - I wouldn’t attempt that.
Why don’t you just change your ticket to go to Korea instead of Narita?