Q: Why can't I lock Notes?

This explains everything.

Keep your notes secure with password-protection - Apple Support

Michael Mortilla wrote:

 

I've sync'd the phone and the Notes are being shared between the devices. Strange...

If you continue to have issues, transfer the Notes to iCloud.

Make sure everything is setup according to this article: Keep your notes secure with password-protection - Apple Support

-AJ

Is your Mac on 10.11.4?

Had you used old Notes (before iOS 9 and/or before OS X 10.11) and failed to upgrade?

iCloud: Updated Notes app

If you have not upgraded Notes since El Capitan and/or iOS 9, here's how to do it on your Mac.

Notes (El Capitan): Upgrade your iCloud notes

It's not the Notes app that needs upgrading.  You have the correct version.

It's the Notes data - your personal Notes.  Have you enabled the new features with iOS 9 and OS X 10.11 that allow underlines, bullets, etc.?

Again, if you have not ...

Notes (El Capitan): Upgrade your iCloud notes

Excellent.  Glad it's resolved.

For what it's worth, having worked with hardware and software from many different manufacturers, I would say Apple software is something that should always be promptly updated.  Each update tends to fix issues, add features, and not introduce new problems because it is well tested before being released.  If you perform many smaller updates instead of fewer very large updates, each change becomes much easier to manage.

Enjoy your Apple gear.