As I understand neon also took a new driver for Intel graphics cards a few months ago. On my system the UI of LibreOffice became a mess as result of that. And I cannot imagine that I am the only one who experienced this.
However, with LibreOffice 5.3 things got better.
Only, I can not "focus" on a cell in calc. There is no black line around the cell when I click on it. When I reinstall the old driver it goes as it should go.
Further there are sometimes unexpected and ugly transparent elements in the sidebar with the new intel graphics driver.

I removed the package libreoffice-kde and installed libreoffice-gtk3.
Libreoffice looks quite different now. Still ugly. But the focus-thing in calc is gone. It works as it should.

Also from the moment the xorg video driver was replaced I had all sorts of complaints with Libreoffice in Neon.
- selected pieces of text were not marked with color,
- there are pieces of the ui you look trough but you should not be able to do so
- pull down menus are often rendered black etc
- the side bar often looks messy.

I tried all kinds of things to fix this but I didn't succeed.
- I installed the 4.10 linux kernel AND I installed the padoka ppa for newer mesa AND I installed xserver-xorg-video-intel-hwe-16.04 but all these things didn't have effect.

A few days ago I tried on the same machine Kubuntu 17.04 and the libreoffice problem was GONE there.
I think issue lies with Neon but I don't know where.
I would like to report a bug but I have no clue what "component" I have to choose. Would that be "plasmash", "kwin"... I don't know.