Filezilla properly downloads files and directories but responds with error when trying to download symlinks to local.
550 Can't open [filename]: No such file or directory
Actually, this is not Filezilla producing the error but Filezilla is just showing the error message from the FTP server. It is likely that the symlink does not resolve to an existing file and the server is therefore unable to provide the file. This can happen since symlinks are just a reference by name, where the named target might exist or not. It can also be that the symlink points to some file outside the root of the FTP server which makes it also impossible for the FTP server to provide the file.
Whatever the reason is: it is an error produced at the server side and you can do nothing in the client to resolve the error.