Hi
No - Apple Watch does not have built-in cellular capability, so it does not require its own cellular service plan and it cannot be locked to any given cellular service provider.
Any cellular services (calls, data) used by Apple Watch are instead provided via the cellular plan on the paired iPhone.
The only lock that can be applied to Apple Watch is Activation Lock. This feature locks Apple Watch to an owner's Apple ID account to prevent unauthorised use of the watch if it is lost or stolen.
If Activation Lock has been enabled on an Apple Watch, then - before selling it, giving it away or sending it in for service - an owner should remove the lock by following the steps here: