LP already has a per-hour email limit. I don't know if there's any per-day limit.
Note that email volume is only one thing that can trigger a spam blacklist. All it takes is one complaint that someone sent spam, or something like SpamAssassin detected spam. It can even happen that someone forwarded their mail (incoming to their LP account), including spam, to another email service (gmail, etc.) and that gets the server blacklisted. I've suggested that LP mandate spam scanning for all email before it's forwarded, but who knows if that will ever happen.