No one here is Autodesk. But we know the following that we are sharing with you.
Your AutoCAD/LT2009 is not supported in Win10, which means Autodesk is not interested ever in helping you with any issue, it does not mean anything else you might read into "supported" http://autode.sk/1IY4C2X
Win10 breaks licenses after OS updates for many users. Microsoft and Autodesk are not interested in ever finding out why. Ever. Not much you can do about it today in Feb2021.
NOTE: Autodesk ended automatic reauthorizing of 2010 and older software as of August 31 , 2019, read all about it here https://knowledge.autodesk.com/support/autocad/learn-explore/caas/simplecontent/content/previous-ver...
But... if you are not using Win10 (or are but still decide to ignore what I wrote anyway) you can open a ticket with Licensing Support and confirm your options for sure here if you must hear it from Autodesk, be careful to listen closely to how they work helping you out if they choose to do so https://knowledge.autodesk.com/contact-support/installation-activation
Remember, no one here is Autodesk, no point in ranting or fussing, we can't do anything about it.
Good luck.