Negative. DDO currently doesn't have anything like lockboxes. However, Lotro DOES. Only you can also pull keys as well besides buying them out of the store.
DDO's closest thing to lockboxes are direct store items as loot in your name. Nothing extra to buy, and loot gems do not effect your chance of store items at all.
As far as I can remember... DDO is also the only one with breakables dropping stuff as well.
Also expect PW/Cryptic to put "special" lootboxes/grab bags in the store being the only way to get certain cosmetics.