I installed Lubuntu 16.04 on an Acer Extensa 2511, 64-bit (then I installed ubuntu-mate-desktop and ubuntu-mate-core). With both lubuntu and MATE, Libreoffice WRITER crashes often, shutting the desktop session down and bringing me back to the login window. I tried to reinstall libreoffice; to remove libreoffice and MATE and to install MATE again,; to reinstall jre. None of these worked. I dont't think the problem is MATE rather than Lubuntu/lxde, this happened with lubuntu as well before installing MATE the fist time. Libreoffice version is 5.1.
So far how I could solve it was by downgrading libreoffice to a previous version. For that I followed this answer: How to "properly" downgrade LibreOffice versions suggested by Cipricus.
I installed version 5.1.1 and it seems to work better.
I removed Libreoffice and installed Openoffice instead, it works fine for me. I'll keep using Openoffice until an update for Libreoffice that fixes the problem will be released.