How can you take off an activation lock?

Activation Lock is designed to prevent anyone else from using an Apple Watch if it's ever lost or stolen.

About Activation Lock on your Apple Watch - Apple Support

Activation Lock is an anti-theft feature that cannot be bypassed. Only the previous owner can remove the lock by using their Apple ID & password. Apple will not help you find the previous owner. If the previous owner cannot or will not remove the lock, then the watch is useless to you or anyone else. Try to get a refund (through eBay) or dispose of the watch properly. In the future, see the 'Before you buy a watch from a third-party' section in:

What to do before you sell, give away, or trade in your Apple Watch, or buy one from someone else - Apple Support

Here is a way the previous owner can unpair the watch if he no longer has the paired iPhone:

• With a web browser, go to: https://www.iCloud.com and sign in with your Apple ID. Open Find My iPhone and select All Devices (at the top). Then click your Apple Watch, select 'Erase Apple Watch', and select Next until the device is erased. Finally click "X" next to remove your Apple Watch.

It's technically possible to pair a watch 1 or 2 to a newer phone,but in reality this is proving almost impossible for just about all the 1&2 owners on this forum.

Newer phone's require the watch to have updated hardware to cope with ios15 and unfortunately because of the age of these watches the hardware is very limited to what it can do.

Then there is the subject of storage,these watches have very little storage space and the average software update now requires gigabytes of space rather than megabytes and again these watches are very limited with the amount of storage space they have.

It is recommended that even a watch 3 should be unpaired and repaired in order to free up enough space to update.