acme-client: Cert-issuance failed because dns resolution for MX-Record failed

When I try to issue a new certificate, I get the following error:

Dns query for an MX record on '<mydomain>.com' failed for the following reason:
All name resolution requests failed in phar:///root/lets-encrypt/acme-client/src/Commands/Setup.php:87

My problem here is, that I have very limited options to debug the acme-client on that particular server, and that dig is able to resolve the particular MX-record.

All of these calls brought proper results:

dig MX <mydomain>.com
dig @8.8.8.8 MX <mydomain>.com
dig @8.8.4.4 MX <mydomain>.com

(It’s a Ubuntu 16.04-Machine)

What options do I have client-wise to resolve the problem? Are there any config-parameters or something? Why is it even necessary to make an DNS-Resolution for the email-address!?