Final answer:
King Lycurgus offended goddesses not associated with war and battle. Goddesses like Athena, who are connected with warfare, were not the ones offended by Lycurgus, as per the fragments provided.
Step-by-step explanation:
The goddesses that King Lycurgus offended were NOT the goddesses who looked over war and battle. This is illustrated in the given fragments where different aspects of ancient Greek deities are mentioned. For example, Demeter and Kalligeneia are associated with agriculture and fertility of the land, but they are not war deities. Likewise, Aphrodite and Hera are related to aspects such as love, beauty, family life, and childbirth, and the Fates with destiny and life's fulfillment.
Meanwhile, the mention of Minerva (Greek counterpart: Athena) accompanied by attendants depicting Terror and Fear, along with the portrayal of the war-goddess promising renown in bravery and triumphs in war, signifies the close relationship this goddess has with war and battle, which is not the domain of the goddesses offended by Lycurgus.