Lag while saving contacts to Note 3

Try logging out your Google account of your device then logging back in and retry
 
I doubt any other 3rd party contact app will help. You mentioned clearing the app cache/data for the Contacts app, but what about the Contacts Storage system app?
B..if the last step doesn't work logging out then back in the Google account , how are these devices with Google apps ,Are they like Huawei?
 
B..if the last step doesn't work logging out then back in the Google account , how are these devices with Google apps ,Are they like Huawei?

I was kind of assuming he was trying to save a contact to the Phone account (rather than Google account).