One of the more fundamental strats in the fight is making sure that a Val'kyr carrying one of your raid members never flies over a Defile. If this happens, none of your melee will be able to dps/stun/slow the Val'kyr, making it difficult to kill her before she drops the person off the platform.
To deal with this, the raid and tank follows a certain pattern. Imagine a clock, with LK's throne at about 12 o'clock. The tank will tank LK near the middle, perhaps just slightly off of center, with LK's back toward 10:00. The raid will tuck in nice and tight behind LK, lined up with roughly 10:00. This way the raid is near the center of the platform, maximizing the distance a val'kyr has to travel. Being clustered tight controls the path the val'kyr takes out from the center.
When LK casts Defile, the person targeted with Defile runs out of the group toward 12:00, and the rest of the raid moves the opposite direction, to help quickly maximize the distance from the person with Defile. The whole raid then sets up in the same pattern as before, but on the other side of the platform, lined up with about 4:00. This forces the val'kyr to travel along 4:00, avoiding the Defile now at 12:00. When the next Defile comes, that person runs to 6:00, while everyone else runs away from them. Repeat.
When the time comes to prepare for the transition to phase 2.5, have the whole raid stay together and follow the val'kyr out as it flies to the edge of the platform. This puts you in an optimal position to jump on the platforms as they reappear.
Dealing with the combination of Val'kyr and Defile in Phase 2 is likely the hardest part of this fight. Get this down solid and LK is in the bag.