About Apple Pay and Apple Watch
For security purposes, adding your Lydia card to your Apple Pay wallet and to your Apple Watch are two separate things. As a matter of fact, your Lydia card will be considered as linked to two different devices.
This means that if you delete your Lydia card from your iPhone, it won't be deleted from your Apple Watch.
However, if you disconnect your Apple Watch from your iPhone, all the cards you added to your Apple Watch will automatically be removed.