The water lock icon does not appear in the control center of my Apple Watch 2.

Hi

The Water Lock feature is only available on Apple Watch Series 2 models, which have a greater level of water resistance than other models:

About Apple Watch water resistance - Apple Support

To check your Apple Watch model - along with your service and support coverage - you can enter the serial number here:

https://checkcoverage.apple.com/

To locate the serial number:

Find the serial number for your Apple Watch - Apple Support

Apple also offers the following resource for identifying your Apple Watch model:

Identify your Apple Watch - Apple Support