This seems the perfect use case for letting a secure BitTorrent tracker share the lists, then either implementing the client in the browser, or having it as a system service that syncs the necessary files.
That being said the data is small so it probably isn't a big deal.
A better solution may be something like IPFS where with a rolling-checksum chunking algorithm you only need to download the changed parts of the list. You could even use IPNS to distribute updates for a fully decentralized setup.