A counter in MTGMagic: The Gathering is permanent. This means it will stay in the game as long as it doesn't get removed by a spell or ability or the card to which it is attached to dies or getsleaves the battlefield (i.e. by dying, by getting exiled, etc.) This means that every Landland on which you decide to put an awakening counter on will stay a 8/8 green Elemental creature until it diesleaves the battlefield or something removes the counter.
Nobody can remove the counter without an appropriate spell or other mechanic as mentioned above.
You should be careful how many Landslands you want to transform. If your opponent has a mass creature destroyer in his hand like Judgement DayDay of Judgment, and he gets to play it, you could lose a lot of Landslands because they are creatures now as well. I played Liege of the Tangle myself a while ago and I adjusted the amount of Landslands I transformed based on the deck of my opponent.