Updated February 6, 2016!
To use Microsoft’s Remote Desktop to connect to a Lubuntu 14.04 machine, use xrdp. xrdp uses vnc4server to spin up LXDE sessions on your Lubuntu machine.
To begin, install xrdp:
sudo apt-get install xrdp
If you try connecting to your machine, you’re going to get a grey desktop. xrdp is trying to use the command “startx” to start a window manager. On Lubuntu, this will not work. You need xrdp to use the command “lxsession”.
To make this change, you need to edit /home/[your_username]/.xsession:
…and make it look like this:
#!/bin/sh /usr/bin/lxsession -s Lubuntu -e LXDE
Save .xsession, reboot your computer, and try connecting from your Remote Desktop client. Voilà!