There are a couple ways you can change your alarm code.
1) If you know your 4-digit master code, enter it into the keypad, then press (8). Type in (02) and then enter a new master code. Enter your new master code again to save the changes.
2) If you don't know your 4-digit master code, you can use the installer code instead. Enter it, then press (8), then (02). Now you can enter your new master code.
3) If you know neither your master code nor your installer code, remove the backup battery and unplug the transformer from the LYNXR-2 panel. Reconnect the battery then the transformer and, while the panel is powering up, press (*) and (#) together. A field labeled "20" will appear. Press (#) to see the current installer code. Write down this number. Press (*99) to leave the programming menu. Then follow the steps above to change your alarm code using the installer code.
The LYNXR-2 is a discontinued wireless alarm panel...
Honeywell recommends that LYNXR-2 users consider upgrading to a newer wireless alarm control panel, like the L5100. This self-contained control panel/keypad will work with all your sensors, plus it can work with home automated Z-Wave device controller if you install the L5100 Z-Wave Module.
ZWSTAT Z-Wave Thermostat