You don't have a "Windows Live ID" anymore—Microsoft retired that brand in 2013. Your Xbox Live Gold subscription is tied to a Microsoft Account (MSA) (email + password). Here is how to locate it.
Use "Forgot password?" on the sign-in page. Reset via email/SMS/authenticator app.
Once signed in at Services & subscriptions, you can:
Note: Xbox 360 requires an Xbox Live Gold subscription for online multiplayer; Xbox One/Series requires Gold for free-to-play games only (most paid games need Game Pass Core/Ultimate).