You can do this through the dconf-editor. If you do not already have it installed, you can install it with:
sudo apt-get install dconf-editor
Navigate to org >> gnome >> desktop >> input-sources
Click in the setting, xkb-options and add 'compose:lwin' inside the square brackets. The single quotes are required.
If other options are already there, the order does not matter; but separate the options with a comma: 'compose:lwin','other:option'
For those who looks for a command line solution (without installing dconf-editor) you can use:
$ dconf read /org/gnome/desktop/input-sources/xkb-options
@as []
This will tell you the current state of the key. Now you can insert your own:
dconf write /org/gnome/desktop/input-sources/xkb-options ['compose:lwin']
This command as above worked fine for me, but @bryce reports that he needed double quotes, as in:
dconf write /org/gnome/desktop/input-sources/xkb-options "['compose:lwin']"
Best Answer
As chaskes pointed out above, you can set the key in Tweak Tool > Typing. There is a fold-out menu named 'Position of Compose Key' which you can set to the key you want.
To activate the changes you may need to log out and log back in.