Running to LVC is a matter of much debate. I often run to LVC and have not seen any significant issues with my packs. Once you cut the motor the voltage usually comes back to about 3.2V per cell or higher, which is well within the safe range.
Don't be alarmed that people don't absolutely agree on everything. Some of these opinions are based on experience, some on recommendations by friends and some based on what has been heard behind the barn. None of the opinions are absolutely right, not even mine. None are absolutely wrong, not even mine.
As long as your LIPOs are at least 3V/Cell when you take them out of the plane you should be fine. So a 3 cell lipo should never read lower than 9V at rest. Best practice would be to have them higher than that. My benchmark is 9.6 or higher for a 3 cell pack.
One thing you MUST be aware of is how your LVC decides what cut-off voltage may be. some are set for specific voltages under load. Typical would be 3V/Cell or 9V on a 3 cell pack. One you remove the load the voltage will come back up some.
Now, some LVC are based on a % of the starting voltage. So if you put in a pack that is charge to 12.6V (3 cell) and the LVC is set for 75% of starting voltage then it will cut the motor at 9.4V under load. Quite safe.
But if you fly for a while, then go back up again it is going to read a partly used pack. That pack may now be at 11.2V. 75% of that will be 8.4V. Now you are getting into the danger zone. That pack will probably come back to about 8.8V when you take it out of the plane. That is lower than you want and, if done often enough, could start to damage the pack.
So, the best practice is always start with a fresh pack so the LVC will cut power at a safe point. Do this and you should be fine. But don't insist on going to LVC. Come down when you can feel the power dropping off.
Of course, your smileage will vary.
To understand more on this and related topics read:
EVERYTHING YOU WANTED TO KNOW ABOUT ELECTRIC POWERED FLIGHT