Does rm -r follow symbolic links

Example 1: Deleting a directory containing a soft link to another directory.

susam@nifty:~/so$ mkdir foo bar
susam@nifty:~/so$ touch bar/a.txt
susam@nifty:~/so$ ln -s /home/susam/so/bar/ foo/baz
susam@nifty:~/so$ tree
.
├── bar
│   └── a.txt
└── foo
    └── baz -> /home/susam/so/bar/

3 directories, 1 file
susam@nifty:~/so$ rm -r foo
susam@nifty:~/so$ tree
.
└── bar
    └── a.txt

1 directory, 1 file
susam@nifty:~/so$

So, we see that the target of the soft-link survives.

Example 2: Deleting a soft link to a directory

susam@nifty:~/so$ ln -s /home/susam/so/bar baz
susam@nifty:~/so$ tree
.
├── bar
│   └── a.txt
└── baz -> /home/susam/so/bar

2 directories, 1 file
susam@nifty:~/so$ rm -r baz
susam@nifty:~/so$ tree
.
└── bar
    └── a.txt

1 directory, 1 file
susam@nifty:~/so$

Only, the soft link is deleted. The target of the soft-link survives.

Example 3: Attempting to delete the target of a soft-link

susam@nifty:~/so$ ln -s /home/susam/so/bar baz
susam@nifty:~/so$ tree
.
├── bar
│   └── a.txt
└── baz -> /home/susam/so/bar

2 directories, 1 file
susam@nifty:~/so$ rm -r baz/
rm: cannot remove 'baz/': Not a directory
susam@nifty:~/so$ tree
.
├── bar
└── baz -> /home/susam/so/bar

2 directories, 0 files

The file in the target of the symbolic link does not survive.

The above experiments were done on a Debian GNU/Linux 9.0 (stretch) system.

To remove the links (from man find under -type):

          l      symbolic link; this is never true if the -L option or the
                 -follow option is in effect, unless the symbolic link  is
                 broken.  If you want to search for symbolic links when -L
                 is in effect, use -xtype.

I think this should do the trick:

find /usr/local/lib/ -maxdepth 1 -follow  -type l

Does the output produce a list of the files you want to delete? If so, when you are 100% sure:

find /usr/local/lib/ -maxdepth 1 -follow  -type l -delete

This will remove only broken links. To delete all links, remove the -follow stanza, but I wouldn't do that under /usr/local/lib.