Moksha is the main goal of human life, people who do good karma attain Moksha.
Is it true that if supreme lord kills someone then she/he will attain Moksha?
The story of Pūtanā is an example
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Yes. Anyone killed by Lord gets Moksha. Lord awards Moksha to even people who hate and reject him. I will give few examples of people who got liberated from Bhagavatam.
These two associates of Lord Viṣṇu — Jaya and Vijaya — maintained a feeling of enmity for a very long time. Because of always thinking of Kṛṣṇa in this way, they regained the shelter of the Lord, having returned home, back to Godhead.(SB 7.1.14)
My dear Prahlāda, O most pure, O great saintly person, your father has been purified, along with twenty-one forefathers in your family. Because you were born in this family, the entire dynasty has been purified.(SB 7.10.18)
An effulgent light rose from Śiśupāla’s body and, as everyone watched, entered Lord Kṛṣṇa just like a meteor falling from the sky to the earth.Obsessed with hatred of Lord Kṛṣṇa throughout three lifetimes, Śiśupāla attained the Lord’s transcendental nature. Indeed, one’s consciousness determines one’s future birth.(SB 10.74.44-45)
Narada Muni explains the reason and purpose to reciprocate love with Lord and reach him.
By enmity or by devotional service, by fear, by affection or by lusty desire — by all of these or any one of them — if a conditioned soul somehow or other concentrates his mind upon the Lord, the result is the same, for the Lord, because of His blissful position, is never affected by enmity or friendship.(SB 7.1.26)
Many, many persons have attained liberation simply by thinking of Kṛṣṇa with great attention and giving up sinful activities. This great attention may be due to lusty desires, inimical feelings, fear, affection or devotional service. I shall now explain how one receives Kṛṣṇa’s mercy simply by concentrating one’s mind upon Him. My dear King Yudhiṣṭhira, the gopīs by their lusty desires, Kaṁsa by his fear, Śiśupāla and other kings by envy, the Yadus by their familial relationship with Kṛṣṇa, you Pāṇḍavas by your great affection for Kṛṣṇa, and we, the general devotees, by our devotional service, have obtained the mercy of Kṛṣṇa. Somehow or other, one must consider the form of Kṛṣṇa very seriously. Then, by one of the five different processes mentioned above, one can return home, back to Godhead. Therefore, one must somehow think of Kṛṣṇa, whether in a friendly way or inimically.(SB 7.1.30-32)
We have two contradicting views for this question, as per two different Purāṇas as follows:-
While in Chapter 1 of Canto 7 in Śrīmad-Bhāgavatam Purāṇa, as explained by Nārada Muni, it is concluded that people killed by a Godhead will definitely attain Moksha, however, in the Skanda Purāṇa, we have verses which say contrary.
According to Chapter 14 - Resuscitation of Dead Daitya, Section 1 - Kedāra-khaṇḍa: of Skanda Purāṇa, those people killed in battle attain the world's of Indra (i.e., Amarāvatī / Swarga-Loka) only, and not the abode of the Godhead (Moksha).
तव युद्धं न दास्यामि नास्ति लोके स्पृहा मम ॥ ७.ख ॥
ये येऽसुरा हता युद्धे अक्षयं लोकमाप्नुयुः । ब्रह्मणो वचनात्सद्य इंद्रेण सह संगताः ॥ ८ ॥
भुंजतो विविधान्भोगान्देववद्विचरंति ते । इंद्रेण सहिताः सर्वे संसारे च पतंत्यथ ॥ ९ ॥
तस्माद्युद्धेन मरणं न कांक्षे क्षणभंगुरम् ।
अन्यजन्मनि मे वीर वैरभावान्न संशयः ।
दातुमर्हसि मे नाथ कैवल्यं केवलं परम् ॥ १० ॥
“I will not offer to fight with you, I have no desire for worlds (and worldly pleasures).
& 9. According to the words of Brahmā, those Asuras who are killed in the battle will attain the Akṣaya (Everlasting) world. Immediately they will come into contact with Indra. Enjoying various kinds of worldly pleasures, they will roam about like gods along with Indra. Then they will fall down to the earthly world.
Hence, I do not desire death in battle. It is of a momentary nature. O heroic lord, it behoves you to grant me Kaivalya (salvation) alone, the great benefit, in the course of my next birth, of course, as a result of an inimical attitude.”
This view is supported by the fact that the Shudra - Shambuka, who was killed by Śrī Rāma, attained Heaven only, as per Chapter 35 - The Killing of a Śūdra Ascetic, in Section 1 - Sṛṣṭi-khaṇḍa of the Padma Purāṇa, and not Moksha.
Although, there's again an 'apparent contradiction' for Shambuka's fate as asked in this question - Did shambuka attain heaven?, because as per Padma Purāṇa Shambuka goes to heaven, but as per Uttara Kāṇḍa of Vālmīki Rāmāyaṇa, he won't attain heaven.
In any case, despite being killed by a Godhead, Shambuka didn't attain Moksha immediately, that's for sure, which supports our View 2.
No,no one gets moksha like that Lord rama killed vali in ramayana, but he was reborn again because lord rama put a debt on himself ,that by killing vali wrongfully vali will be reborn to get that karma balanced. This is the reasoning behind the deathof lord krishna who died by the arror of vali's reincarnation.
The laws of karma are not something lord can bend. If you wanna write citations than you can find argument in favour of the question and some against. But you must think for yourself too. Many believe you will attain vaikuntha if you donate a cow because it is written in mahabharata and other smriti text but we know better about this.