So, what's the alternative?
Now it's your choice... you either lose B but protect the rest of the infrastructure from hackers... or you think the CVE doesn't apply to your usecase (internal thing on a testing server), and don't upgrade L to keep B working.
You can also install both versions of L. You can also patch the broken part of L out at the old version, if it's not mission critical. There's a lot of things you can do.
Having one giant binary file with everything statically compiled in is worse in every way, except for distribution-as-a-single-file (but you can already do this now, by putting the binary and the libraries in a single zip, dump everytinh in /opt/foo, and let user find the vulnerable library manually... which again, sucks.