Should my local::lib settings go into my ~/.bashrc or ~/.profile?

I don't think there's any one-size-fits-all answer to this question, as various (site/system/distro-specific) shell startup file policies are being used.  One common approach is to source .bashrc from the login profile (.profile), and then put the common stuff (i.e. what you want to have in both login and non-login interactive shells) in .bashrc, and any additional initialisations you want only for login shells in .profile.  In case this policy is in use, .bashrc would be the appropriate place to put the local::lib settings.

Note also that there is a third "type" of shell - non-interactive - which by default doesn't read any startup files (but of course inherits the environment from where it's called). The latter is used to run commands via -c.  Also, the details vary widely from shell to shell... For bash-behavior, see the INVOCATION section in its man page.