I think it would be interesting for lockboxes to drop bonus quests. Give these quests a better chance of dropping from the lockbox than the premium item itself. Completing the quest would give you a reward, such as a premium item, recipe, or crafting material. Make the quality of the reward dependent upon the difficulty of the quest.

Have the more difficult quests requiring skill, perseverance, or help from other players drop the best rewards. Other, less rewarding quests can be simple treasure hunts. For the best quests, the reward can be setup so that it can be shared with raid members, similarly to how rewards are shared for raid rifts.

Have the quest theme be aligned with the lockbox it drops from. For example, a quest dropped from a Greenscale lockbox might involve descending into Greenscales Crater to collect some items or defeat the zone boss.

I think this will make the lockboxes a little more interesting. It will increase a players chance of getting an interesting reward, but only if you work for it, while providing something unique to do with friends and guildmates.