Is there a way to whitelist the Googlebot?
Unfortunately problem not. Google does not publish its IP ranges, so you cant whitelist google.
I get DNS lookup errors, Network unreachable and more errors due to ASL Lite. No, it's not a DNS issue, only 2-3 errors per day.
I'm not sure I understand your issue, perhaps you can expand upon your issue. ASL Lite is just a license to use our real time modsecurity rules, and the apache modsecurity module has nothing to do with DNS on your system nor can I think of any way an apache module could ever affect DNS lookups. Is there some reason you believe an apache module is affecting DNS on your system? I can't think of any way Apache could ever do this, so please let us know.