Would be interesting to hear what database they are using and how they are doing replication? Is it simple master / slave or multi-master?
https://github.com/letsencrypt/boulder
You can find a docker-compose.yml file to get some idea.
Appears to be using MariaDB.
They shut down OCSP responders and expiry email reminders, so there really is no need to have a database apart from rate limits, auth data, and caching.
For Certificate Transparency, they are submitted to Google and CloudFlare run trees but I don't think LetsEncrypt run their own logs.
Let’s Encrypt currently has a single primary with a handful of replicas, split across a primary and backup DC.
We’re in progress of adopting Vitess to shard into a handful of smaller instances, as our single big database is getting unwieldy.