Trample
Whenever Liege of the Tangle deals combat damage to a player, you may choose any number of target lands you control and put an awakening counter on each of them. Each of those lands is an 8/8 green Elemental creature for as long as it has an awakening counter on it. They're still lands.
If an awakening counter is moved from an affected land to another land, this doesn't cause the recipient to be affected by Liege of the Tangle's ability.
Whether an affected land remains an 8/8 green Elemental creature depends only on whether it still has an awakening counter on it, not on whether Liege of the Tangle is still on the battlefield.