Bukkit

This is the definite fix for UUID appearing on signs. Make sure you have the latest ProtocolLib installed on your server.

However due to a ProtocolLib bug (?), this fix does not and not possible to work on spigot 1.9.2.

STOP - PLEASE READ BEFORE USING UUID SUPPORT TO 2.x (UUID)

Dependency
https://www.spigotmc.org/resources/protocollib.1997/ProtocolLib if you use UUID support.

Shall I enable UUID support?
This really depends. If you want players to be able to access their locks after they change their names, turn it on. If you hate players changing names because they will confuse others or potentially break other plugins, turn it off.
I have tested UUID support feature several times and maybe this works perfectly. In case you are hesitated about the consistency of UUID support, you can hold for just a few days before turning it on.

How to turn on UUID support? Is it on by default?
UUID support is turned off by default. The config line to turn it on is "enable-uuid-support: true". If your config.yml is missing entries, you may add them manually referring to this detailed guide, or delete config.yml and let it regenerate.

How does UUID stored on the sign?
Detailed information is available on GitHub wiki page.
TL;DR: Storage format is "username#uuid", for instance, "connection_lost#15e68dc9-5454-411a-8023-668b3877fe9b". Also, client will not see the uuid (those characters behind "#") so the signs will always be clean.

How signs will be updated?
If you choose to enable UUID support, all new lock signs will be contain UUID information, and old signs will be updated upon the valid user is interacting with the block or sign.

What will happen if I turn off UUID support?
Unfortunately, there is currently no way to just convert all UUID lock signs to normal signs. If you turn off UUID support in the future, all signs will be treated as normal name lock signs even UUID are present. LockettePro will correctly interpret those signs, but original Lockette cannot.