That was indeed the problem, I just figured before reading your message.
After Bee-liever's tip, I still looked it up and found out that the .dll file should also be in the SysWOW64 folder if you're running a 64-bit OS, which is my case. Since it wasn't there, I copied/pasted the file from the System32 folder.
When I tried to encode again the DLL error message didn't appear but another one did, telling me that lame.exe couldn't start properly.
In MusicBee properties, lame.exe is located within the software's Codec subfolder so I changed the location to the lame.exe I had installed myself a while ago and now the encoding works!
Thanks to both of you.