As the title says, the Lore strings cannot be formatted as json, it'll just show the direct string:

example, use:

give @s stick{display:{Lore:["{\"text\":\"Hello\"}"]}}

Side note: a new function may want to be added for loot tables, for the same reason as the set_name function got added.
Side note 2: might as well be changed to a single string rather than a list of strings.