Flygon lock aims to trap something that can't attack in the active position either through SW Trapinch's Inviting Trap (its attack is used by Flygon lv. X via Memory Berry) or Palkia lv. X, and Sand Tomb. While that Pokemon is stuck active, Flygon lv. X sits there and discards cards from the opponent's deck until they're either out of cards or, if Flygon is ahead or even in prizes prior to the lock (which is a good idea in case a deck-out isn't possible under time constraints) and time is called, the Flygon player finally attacks big and takes the game-winning prize.
Palkia G lock is based around abusing Mesprit via Palkia G lv. X's Lost Cyclone, which prevents the Pixies from cluttering your bench. Between Power Spray and Mesprit, up to 8 turns of Power locking are possible, hampering virtually every deck. Then, Palkia G lv. X has Hydro Shot to take out any shielded Pokemon being built on the bench, or Claydol (it is shut down for a long time and then, when the lock has to break, it is sniped out of the picture). Luxray GL lv. X is a common card in variants of this deck for added disruption.