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I'm not aware of any Ubuntu process that would remove a manually copied library from /lib/x86_64-linux-gnu except in order to replace it with one from an installed/updated package. However the appropriate place to put such libraries would likely be /usr/local/lib - see for example 4.9. /usr/local : Local hierarchy in the Linux Filesystem Hierarchy Standard. You may need to run sudo ldconfig after in order to add the library to the runtime linker cache.
sudo ldconfig
after in order to add the library to the runtime linker cache.