LE is using the default libc resolver and this caches records according to their TTL values so I doubt caching is the issue. I'd make an educated guess that Kodi makes some form of discovery request which is being denied or sinkholed by Pi Hole and so the request is being repeated (ad infinitum) hoping to get a response (which never comes). There is probably something in Kodi that could have better failure logic. In the same breath Pi Hole improvement to not break the world's most popular mediacentre app would be a good thing too. The decision to use Pi Hole also makes it a self-inflicted problem, sort of, so both sets of developers will probably point fingers at the other.
More verbose logging from Pi Hole and/or perhaps a PCAP of the traffic to look at would be useful.