Anuttamā अनुत्तमा (541)

No one is superior to Her, an exclusive of the qualitiy of the Brahman.

This situation is best explained in Śvetāśvatara Upaniṣad (VI.8) which says “No one is His equal; no one is superior either.  He possesses many gifts of a high order.”

The same situation finds a place in Bhagavad Gīta (XI.43). “Unparalleled by any other in the three worlds, who may surpass Him, the Lord of power incomparable.”

Anuttamā also means intellect not derived from others.  She is the embodiment of intellect. 

Puṇyakīrtiḥ पुण्यकीर्तिः (542)

She is known for virtues.  She gives fame to Her devotees.  The very thought of Her, sanctifies a person. 

Viṣṇu Sahasranāma nāma 688 is Puṇyakīrti which means He is capable of eradicating sins of His devotees.   

Puṇyalabhyā पुण्यलभ्या (543)

She is attainable through virtues.  Puṇya means virtues.  It is said that ‘She is attained by those who are virtuous and have knowledge of Veda-s.  Those who are desirous do not see Her.’

Saundarya Laharī (verse 1) explains this.  ‘You are worshiped even by Brahma, Viṣṇu and Rudra. Unless one has accumulated virtues of previous births (good karma-s), how can anyone be capable of singing Your praise or prostrate before You.’

Puṇya-śravaṇa-kīrtanā पुण्य-श्रवण-कीर्तना (544)

Recitation of verses in praise of Her (like this Lalitā Sahasranāma), or listening to such praises are virtuous acts. 

Viṣṇu Sahasranāma 922 conveys the same meaning. The uttara-bhāga (the concluding part) of Viṣṇu Sahasranāma verse 2 and the concluding part of this Lalitā Sahasranāma also conveys the same meaning. 

Pulomajārcitā पुलोमजार्चिता (545)

Indrāṇī is the wife of Lord Indra and Her father is known by name Puloman.  She is an ardent devotee of Lalitāmbikā.  This nāma is included in this Sahasranāma to highlight the importance of morality and the benefits attained on worshipping Lalitāmbikā.  This nāma means that She is worshipped by the daughter of Puloman, i.e. Indrāṇī

There is a story in Devi Bhāgavata (chapter VI) which goes like this: There was a demon by name Puloman.  He had a daughter known as Śaśī. Indrā killed Puloman and married his daughter Śaśī. Thus, Śaśī became Indrāṇī. Indra befriended with another demon by name Vṛiddāsura.  Vṛiddāsura’s father Dvaṣṭā forewarned his son not to entertain friendship with Indra.  As the fate would have it, Vṛiddāsura did not listen to his father’s advice.  At an appropriate time, Indra killed the demon with the help of Lalitai, Viṣṇu and others.  Since Indra killed his friend through foul means, he was afflicted with brahmahatyā doṣa (sins accruing on account of murdering a Vedic scholar) as cursed by Dvaṣṭā.  Nobody came to his rescue.  When Viṣṇu and Lalitai helped Indra, everyone helped him.  But when Viṣṇu and Lalitai were no longer willing to help him, none came forward to help him.  As a result, Indra left his empire, came to the earth and started living in a lotus stem.  Nobody could find him.  The absence of Indra was felt in the universe.  There was no rain which resulted in acute famine all over.  Demigods, goddesses and sages appointed a demon by name Nahuṣa for the post of Indra, to overcome the famine.  Nahuṣa, impressed by the beauty of Indrāṇī wanted to flirt with her.  Knowing this Indrāṇī went to Brahma.  He could not offer a lasting solution.  Then along with demigods, etc Indrāṇī went to Viṣṇu for a solution.  Viṣṇu advised all of them to worship Parāśaktī.  With Her grace, Indra was found by Indrāṇī.  Indrāṇī told Indra that her chastity is in jeopardy with Nahuṣa occupying Indra’s throne.  Indra told her that their time is not auspicious and that she should go back to Indraloka.  He also told her that to protect a woman’s chastity nobody can be of help except her own will power and determination.  She went back to Indraloka and told Nahuṣa that she would oblige him if he comes to her place in a palanquin carried by the seven great sages (sapta riṣi-s).  Accordingly, Nahuṣa summoned sapta riṣi-s.  Sapta riṣi-s obliged Nahuṣa as they were aware of what is in store for Nahuṣa.  Out of the seven riṣi-s, Agastya was very short and when he walked with the palanquin, it tilted towards his side.  Angered by this, Nahuṣa beat Agastya and kept his foot on his head.  Agastya is a very powerful sage who had once consumed the entire water of all the oceans.  Agastya cursed Nahuṣa to become a python and immediately he fell down in a forest with the body of a python.  Knowing this, Indra returned to his kingdom.  Indra was restored to his throne with the grace of Lalitāmbikā.