A website opens every time you unlock the phone? You may have downloaded some malware or installed an app that's doing that. Boot the phone into safe mode. If the phone stops doing that, then you'll know it's caused by a third-party app you installed. You'll have to figure out which one and uninstall it. Start with any "free" apps or games.
Did you set the site as your home page? Do you have your settings set to open with last open tab? Regardless of which browser you use, they all have a setting to set the home page or whether the app will open with a blank page.
