Find phone

On what account?

You can use the Find My iPhone App to track any device that is logged in to iCloud using your Apple ID.

If its not using the same Apple ID as your other iPhone, then you would need to log in to the Find My iPhone with the Apple ID that is being used on the lost iPhone for iCloud. Only log in to the App, nowhere else.

See here: If your iPhone, iPad, or iPod touch is lost or stolen - Apple Support

Being on your same cellular service account has no bearing on tracking it.

You may get better and prompt responses if you kindly provide the iPhone Model that you have with iOS version if it is known to you.