Let's Encrypt still has to publish OCSP responses for every non-expired leaf certificate, at least in time that you can always get a new OCSP response before the previous one expires. In practice they have a tighter schedule so that there's a period between "We are not meeting our self-imposed deadline" and "The Internet broke, oops" in which staff can figure out the problem and fix it.
To do this they automatically generate and sign OCSP responses (the vast majority of which will just say the certificate is still good) on a periodic cycle, and then they deliver them in bulk to a CDN. The CDN is who your client (or server if you do OCSP stapling, which you ideally should) talks to when checking OCSP.
To generate those responses they need a way (hey, a database) to get the set of all certificates which have not yet expired and whether those certificates are revoked or not.
To do this they automatically generate and sign OCSP responses (the vast majority of which will just say the certificate is still good) on a periodic cycle, and then they deliver them in bulk to a CDN. The CDN is who your client (or server if you do OCSP stapling, which you ideally should) talks to when checking OCSP.
To generate those responses they need a way (hey, a database) to get the set of all certificates which have not yet expired and whether those certificates are revoked or not.