The DNS provider needs to provide an API, but not an ACME server.

Your server contacts Lets Encrypt and wants a certificate - say for homeserver.example.com. It tells Let’s Encrypt to use DNS based authentication. Let’s encrypt answers with a challenge code, that you now publish as a txt record with a defined name via your providers API for this (sub)domain. Let’s encrypt then checks the TXT record and if it finds the challenge there, it sends you the certificate.