An eagle lectern flatpack is an unobtainable item. It was most likely intended to be released alongside Construction as a flatpackable version of the eagle lectern, but was scrapped before launch for unknown reasons, alongside other flatpackable versions of various furniture in the Study.
Upon the release of the Grand Exchange, players were able to submit buy offers for these items, but as they cannot be made in the workshop's workbench, the offers were never completed.
When asked about these items in a Q&A stream on 24 March 2016, Jagex Moderator Mod John C gave the following response:
||There's a number of flatpacks that exist as objects in the game but you can't actually create them, because they were created when Construction was being developed as a skill way back in... 2005? 6? The flatpacks that exist were scrapped but the objects weren't deleted, so they made it into the live game... we could make them flatpackable, but there's no real benefit to it.
— Mod John C, Associate Producer
The items were then removed from the Grand Exchange in an update on 14 April 2016.