Well, imagine you're in a controlled environment (eg, China) and having your non-vpn IP leaked could compromise your identity. Having an easy way for a site to reveal you is therefore a security issue.
Even if he is, it's still information that doesn't need to be revealed. It's not a security issue in and of itself, but if combined with another exploit, it could help an attacker. Good security is all about layers and protecting information.
LAN IPs are also useful for distinguishing computers from the same external IP which could help compromise your identity or privacy.
