You can't "lose" an Apple ID, unless what you mean by that is you forgot it.
Basically you have to know it in order to recover it. You can't type your name into a search field and it will tell you the Apple ID for that name (that would be a huge violation of privacy). Typically an Apple ID is an email address you have used. If you are currently using a mobile device that is logged into your account, go to Settings and tap your name at the top.
Look in Keychain, and in a browser's security settings if you use it to automatically sign into Apple when using a browser.
This support article describes ways to find your Apple ID --> If you forgot your Apple ID - Apple Support
or go directly to this link --> https://iforgot.apple.com/appleid
If you still need help:
Contact Apple for help with Apple ID account security "This article provides country-specific Apple Support contact information for customers seeking help with their Apple ID password or other security-related issues."
Contact Apple for support and service - Apple Support