Angelplayer's directions are great. Except be sure your note is in iCloud Notes. If the note has options to handwrite on it (a squiggly button in the bottom toolbar of the note), then it is in iCloud; otherwise it is not.
If you use Gmail or another non-iCloud service to sync your notes, Apple will not let you lock them (they would still be visible in Gmail and Apple does not want to give you false confidence about the secrecy of the notes).
How to set up iCloud Notes: Go to Settings on your iPhone/iPad, tap iCloud, then toggle on Notes.
Once your notes are synced with iCloud, you can tap the export button in the top left of a note and tap "Lock Note."