Google analytics can be sometimes hard to understand, and now with Facebook you are seeing different kinds of referring sources as you might have seen. So here’s the difference
Referral traffic from l.facebook.com or lm.facebook.com are from facebook users clicking on sponsored shared links.
The difference is: l.facebook.com is when someone clicks a shared link from facebook desktop (or on a device in desktop mode) and lm.facebook.com is when someone clicks a shared link from the mobile Facebook version (m.facebook.com).
As you can see from the stats below, this clients followers mostly access information from their mobile devices, another reason why a responsive, mobile friendly website is essential.