Zimbra Version: Release 8.6.0_GA_1153.RHEL6_64_20141215151155 RHEL6_64 FOSS editio
Change user to zimbra and stop proxy(error if not used, it's ok) and mail box service before renew proccess. It's necesery to stop this two services because letsencrypt and this services are working on the same 443 port.
su zimbra
zmproxyctl stop