Don't know Lightroom, but two ways I sometimes make "notes" about an image using Photoshop/Bridge.
One is with the "Note" tool inside Photoshop. That's hidden under the Eyedropper tool. Notes are seen in the Notes window, and an icon is added to the image to remind you there is a note. But the note does not display in any browser (Bridge). I sometimes use this to make notes about editing steps before flattening and saving an image.
Another is to add a description in the IPTC data block. The description can be added inside Photoshop via File/File Info. It can also be shown and edited in Bridge metadata. This is where I usually add printing notes. Example: "Costco print version, s-curve added".
Unfortunately, neither of these methods allow for searching or filtering images that have notes.
I frequently and extensively move my images around from folder to folder and to various backups. Notes embedded inside the image follow them wherever they go, unlike in a central database like Lightroom.