The Lock Screen flow is different from the Home Screen one and catches people out, because it starts from the Lock Screen itself rather than from Settings. Wake the phone, press and hold the Lock Screen until the Customise button appears, tap it, then choose Lock Screen. The slots under the clock are the widget area — tap one, find WidgetNote in the list, and add it.
Lock Screen widgets are much smaller than Home Screen ones, and they are rendered in a flat tinted style rather than in your paper colors. That means the styling work you did on a note largely does not show here, so the Lock Screen is best for the shortest possible note: a time, a code, one word. Anything longer belongs on the Home Screen where the full note design is visible.
It is also worth knowing these are separate placements. A note on the Lock Screen does not remove it from the Home Screen, and both can point at the same note or at different ones.