The issue as it stands is the incredibly low drop rate for gear in LFR. Now I understand why the drop rate is low, basically if blizzard significantly increased the drop rate then people would burn through the content, gear up super quick and get bored and complain or worse (unsub). That said there is also the real concern that unlucky players can currently run LFR weeks on end without a single drop which can also be very frustrating.
So that leads me to my suggestion. I think blizzard could incorporate a "karma" system behind the scenes. Basically this is how it would work.
Every time you defeat a boss in LFR and you don't get loot you get a Karma Point added to your account behind the scenes. What a Karma Point would do is add X number to your next loot roll. Here is an example.
Let's say for arguments sake you need to roll an 80 or better behind the scenes when a boss dies in LFR to obtain a piece of loot. Now let's say for example each Karma Point you earn adds 5 to your internal loot roll. So using those numbers assuming you kill 10 bosses in a week without getting loot that would mean you have built up 10 Karma Points and that would add 50 to your next internal loot roll (meaning you would only have to roll a 30 or better behind the scenes to win a piece of loot). As soon as you won a piece of loot your Karma Points would reset to 0. Obviously these are made up numbers and blizzard could tweak as they see fit.
So, how does this change LFR loot? It simply means the longer you go without getting a piece of loot the better your chances will get for obtaining said loot. This would eliminate the situation where you can conceivably go weeks (or longer) running LFR without a single drop but still spread out the time it takes to get geared up.
FWIW this idea came from an old loot system that I used to use for raiding called NI Karma where every boss you killed gave you karma points which you could use to add to your roll when rolling for loot. Once you used your karma bonus you lost all your karma points and started over.
For reference: http://www.wowwiki.com/Ni_Karma