Any lairs you have purchased will be available in-game. Later on in Alpha, you will have to place a DOOR to your lair in an appropriate part of the world, but for now you can teleport by accessing the Lairs Tab and using the TELEPORT button.
You can find the Lairs tab on the second from the right on the quickbar at the top of the screen.
Inside the Lairs option, you will see any lairs you are allowed to access. If you buy a new Lair, be sure to log out and log back into the game.