Meaning of Krishna's advice to Yudhisthira before Drona Vadh

Question

With popular belief Krishna advices Yudhisthira to tell lie to Drona about "Killing of Ashwatthama" for the sake of saving remaining Paandava army from being annihilated.

But according to this text, it appears much broader:

Govinda, knowing that Drona, that foremost of warriors, was capable of sweeping all the Pandavas off the face of the earth, became much distressed. Addressing Yudhishthira he said, 'If Drona fighteth, filled with rage, for even half-a-day, I tell thee truly, thy army will then be annihilated. Save us, then, from Drona. under such circumstances, falsehood is better than truth. By telling an untruth for saving a life, one is not touched by sin. There is no sin in untruth spoken unto women, or in marriages, or for saving king, or for rescuing a Brahmana. 1

Footnote 1: This verse is omitted in the Bombay text. There can be no doubt, however, about its genuineness.`

Is the part shown in bold really authentic? If yes, why women and marriages are covered?

Answer 1

From the text quoted in this answer, I got the answer finally.

Like how we are mistaken to equate "killing = violence" due to its nature, we often mistaken "correct information" as "truth" and "incorrect information" as "falsehood". But Krishna clarifies it to be "utter-able" and "unutterable" respectively:

Behold, however, truth as practised is exceedingly difficult to be understood as regards its essential attributes.
Truth may be unutterable, and even falsehood may be utterable where falsehood would become truth and truth would become falsehood.

Had Yudhishtira told Drona about his son was not dead, then he would have just given the "correct information" like a machine. After that Drona would have killed the whole army of PAndavas. In such case a side will be victorious, which subscribed to treachery (dice game), murdering (LAkshAgriha), molestation (Draupadi's insult), renege (denying kingdom after 13 years). This would have caused deterioration in the society under such regime.

Suppose, you have a high standard of taste being a restaurant owner. A relative invites you for a meal with compassion and feeds you terrible food. If asked, "How was the food?", would you say: "Terrible"?
No! "Terrible" is just a correct information, which describes the food. But "dinner invitation" is not limited to food alone, it involves the "compassion" as well. In such case, you may want to lower your standard for "food" and say it was "Good"!
Above also doesn't mean that, you should blindly follow others' emotion beyond threshold. If the other person expresses an interest to become the chief cook in your restaurant business, then ofcourse your priority will change from "saving emotions" to "saving jobs"! :-) In such case "correct information" becomes "truth".

Some patients are not informed the computer generated "correct report" that he/she has cancer. That's Not falsehood, because if told it may create distress on sensitive person. Rather his/her relatives by saying "everything is OK", allows the patient to live a less stressful life. That becomes the "Truth".

In general, "truth" is not limited to information, but also how broad purpose it serves. We need to have discrimination, that we are not using "incorrect information" for limited/selfish purpose.

"... why women and marriages are covered?"

This seems just an example, where you may have to often practice differentiation of "truth" vs "correct information". That is explained in subsequent para:

On an occasion of marriage, or of enjoying a woman, or when life is in danger, or when one's entire property is about to be taken away, or for the sake of a BrAhmana, falsehood may be uttered.

Answer 2

The part in bold from Droṇa-parva is missing from the Critical Edition of the Mahābhārata. Here's how it reads in Bibek Debroy's translation based on the CE:

Chapter 1141 (64)

...

He [Drona] was tormented and pained and asked Yudhishthira, Kunti's son, whether his son [Ashvatthama] had indeed been killed or not. Drona was firm in his mind that Partha [Yudhishthira] would not utter a falsehood, even for the sake of all the prosperity in the three worlds. It is for this reason that he asked him and no one else. Since the days of childhood, he had always hoped to hear the truth from Pandava. Knowing that Drona, the lord of a battle, was capable of emptying the earth of the Pandavas, Govinda was pained and spoke to Dharmaraja. "I tell you truthfully that your army will be annihilated. Save us from Drona. In this situation, falsehood is superior to truth. If one utters a lie for the sake of saving lives, one is not touched by the taint of falsehood."

When they were conversing, Bhimasena said, 'O great king! As soon as I heard about the means for killing the great-souled one, I immersed myself in the Malava soldiers of Indravarma. There was an elephant named Ashvatthama and it was like Shakra's elephant. Exhibiting my valour, I killed it in the battle and told Drona that it had been killed. "O brahmana! Ashvatthama has been killed. Stop fighting."

...

No mention of lying to a woman (lover) or for the sake of marriage.

However, the verse itself seems authentic as it's present in Manusmṛti and Medhātithi's commentary clarifies the intent behind such lying.

Manusmṛti 8.112

कामिनीषु विवाहेषु गवां भक्ष्ये तथेन्धने ।
ब्राह्मणाभ्युपपत्तौ च शपथे नास्ति पातकम् ॥ ११२ ॥

kāminīṣu vivāheṣu gavāṃ bhakṣye tathendhane |
brāhmaṇābhyupapattau ca śapathe nāsti pātakam || 112 ||

There is no serious offence in swearing to women, or in connection with marriages, fodder for cows, or fuel, or for the sake of a Brāhmaṇa.—(112)

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Medhātithi’s commentary (manubhāṣya):

‘Kāminīṣu’—‘Kāma’ is a particular form of pleasure caused through the tactile organ; and those who are productive of such pleasure are called ‘Kāminī,’—which is a terra that stands for wife, courtesans and so forth. To these if one swears, for the fulfilment of his desire—in such words as ‘I do not love any other woman, thou art the queen of my heart,’ etc., — there is nothing wrong in this; though, if after meeting the women, and on being asked by her to give a certain thing, he swears falsely that he would give it to her, — then this is certainly wrong.

...

‘In connection with marriages’; — when one says ‘this man has married another woman,’ or ‘that woman should be married by you,’ and so forth; such lying, also in connection with the marriage of friends and others, is not sinful, but not so the concealing of the real caste of the bride and such details.

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Explanatory notes by Ganganath Jha

This verse is quoted in Smṛtitattva (II, p. 229), which adds the following notes:— ‘Kāminīṣu,’ when conversing with a woman in secret one may swear falsely for the purpose of satisfying her; — similarly for the purpose of bringing about a marriage, for obtaining food for cows, for obtaining fuel necessary for offerings, and for saving a Brāhmaṇa; — and in Vyavahāra-Bālambhaṭṭī (p. 406).

As for marriages, there is a popular saying in South India which goes like 'help arrange a marriage even if it means you have to tell a thousand lies.' The verse from Manu maybe the source of this. I don't think the intent is to dupe either party involved in the marriage but to bring two like-minded individuals/families together.