hmmm too summarize, the way I understand the whole thing :
Zimbra only supports "Inline Attachments"
iCal and Mozilla Thunderbird / Lightning only support "External Attachments"
As far as I understand the RFC this is good for Zimbra in way because they provide the required feature to conform to CalDav ("CalDAV clients MUST support inline attachments ... . CalDAV servers MUST support inline attachments).
Funnily if this is the case then I wonder, why Apple isn't properly supporting their own RFC requirements in iCal. For Thunderbird/Ligthning there has been an according Bug Report open for 9 years now
Bug 168680 however, work on this now seems to be progressing in the last few months, so we hopefully have compatibility there soon)
Another possibility would be Zimbra adding support for external Attachments (rfc4791#section-8.5.2) too, so that it would work at least in this way with the clients existing capatibilites. However this seems unlikely as this
Zimbra Bug is marked invalid. Even though I'm not sure why, because the way I read the RFC, inline and external attachments are not mutually exclusive ?!