The Living Archlight Token, sometimes referred to as LAT is one of the most expensive currency's in the game. You can only obtain this token through donating a certain amount in the donation shop. The Living Archlight Token is also used to purchase rare items at Living token Exchanger at the ground level of the depot.

So if anyone ever refers to LAT, they mean a Living Archlight Token.

The Archlight Token is one of the main trading currencies, and what most things in the market sell for.
And if they say AT, they mean Archlight Token.

Archlight Tokens are obtained through Personal and Greater Dungeons, Story Quests group and solo, Arena, Ritual Lords, Etc.