Epub3 can be for different purposes. That will be separately considered, or you can epub2 to epub3 and add extra epub3 stuff.
Old Open Office /LO had a plugin. It was poor.
I compared LO Writer 7.4 used with Calibre 7.4 to make an epub2.
LO Writer direct export epub offers epub2 or epub3. Many of the chapter headings lose text in the TOC. The files are bloated with <span> tags within paragraphs. It's still useless.
Back in LO 5.x and Calibre 6.x the best option was an extra Save As in docx and convert that in Calibre to epub2.
Using LO Writer 7.4 Currently it looks OK, but the H1 to H3 are replaced by styled <p>, though page/file breaks, internal links and TOC is OK. I was sure it used to do H1 to H3 etc. It may be the conversion for Save As in docx is the issue. I'll test with MS Word later. The LO 7.4 certainly seems buggier than the 6.x I was using.
Currently using the LO Writer 7.4 odt direct with Calibre 7.4 is working better than docx. The headings are correct <hx> where x is heading level in LO Writer paragraph style. The 6.x odt to older Calibre epub2 erroneously used list format instead of <h> for headings.
It's puzzling and as Kovid suggested the odt import wasn't being updated, I suspect the changes are in LO Writer 7.4 version.
Next I'll look at images, where the CSS has always needed checking unless the image is pixels in source to px in CSS with no "auto".