It appears as though using the Debug Stick on a Lectern does nothing at all. It seems to work on nearly everything else appropriately.
To replicate:
1: /give @s minecraft:debug_stick
2: Place a Lectern
3: Try to change the Lectern values with the Debug Stick.
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Bugs relating to the debug stick are not supported on the bug tracker.
marcono1234
The underlying issue seems to be MC-197944. It looks like the debug stick works if you hold shift while clicking the lectern.
Upon trying this on another 1.16.1 server, it seems to work properly. Unsure of what happened to get it to not work.