Having been a maintinance manager for a large company in Deleware for many years, I've rekeyed many locks in several apartmeent complexes across the state. (Maybe as many as 5,000 apartments?) Every time someone moved out, the locks had to be rekeyed for individual keys and a master key.
If your night latch key will go into your new lockset, it can be rekeyed for one key to work both locks. Once you get the hang of it, it only takes about 10 minutes.
Once you have disasembled the lock, gently remove the small plate covering the cylinder pins or tumbler pins. Once the pins are exposed, you just need to hold the cylinder flat, and use a file to file the pins/tumblers down flush with the cylinder while the key is inserted. When filed down smooth, your key should work both locks. Once you've done a few locks, you'll have several different length pins/tumblers. Then you can rekey the lock to several different keys for the same lock.
When you're done, simply reassemble the lock, putting the retainer plate back on and put the cylinder back in place.