The way things sit right now, this is unlikely to ever work.
There are two major issues:
Lightdm is setup to run under the
Xorg windowing system, as is the version of Chrome that you mention. While Xorg will run on the Pi, there are not currently accelerated video drivers, so performance will be painfully slow.
The Chrome software you mention is not ported to the ARM CPU architecture. There are other browsers and window managers and login managers that are, but you would need to assemble a software stack that did work, which would be different than your original question.
So, no. There are ways to setup a browser centric desktop experience on a RPi, but you should forget about that particular software stack unless you want to do a serious amount of porting. If you knew how to do that, you wouldn't have asked this question.