If you add lore text to a Minecart with a program such as NBTedit, after the Minecart has been placed and broken it will no longer retain its lore text. However, the Minecart will still keep attributes such as names added using an anvil.
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I know that they are not capable of keeping lore text. When a minecart is used on a rail by right-clicking, the item is deleted and it spawns an entity on the rail in the location that the player clicked on. It is capable of spawning with some of the same attributes as the item. However, when it is broken, the entity will delete itself and spawn an item on the ground. Minecarts do not yet have the ability to recognize lore text in its entity form, so they drop themselves without that data. However, they can be programmed to have that data saved when they are in an entity state. You were probably going for "it isn't a bug, because that feature is not implemented yet," so you are correct in that this would be better marked as a feature request. However, I found that if the entity is capable of retaining its name, it should also be capable of retaining its lore text, as they are both displayable in the inventory.
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Only three entities can seamlessly switch between inventory and in the world; arrows, boats, and minecarts. Technically speaking, yes, entities have the ability to have a lore tag, but they don't, and it's because they were programmed not to. If you want to change how it is, suggest it on the Forums or Reddit. I just linked to MC-209 because it's the same reason; items, entities, tile entities, and blocks are not the same thing. They do not share the same NBT tags most of the time, and so are not often persistent.
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Is this still a concern in the current Minecraft version 1.7.2 / Launcher version 1.3.4 or later? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.
Ezekiel
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I can confirm, but for minecarts, names are kept. Enchantments are lost. Also, boats lose both enchants and names.
Same/similar issue as MC-209
Items are not the same as entities. Entities do not have lore tags, but they do have name tags. So a Minecart (or boat) can be renamed, but it can't keep it's lore.