Is lying adharma? What do Kṛṣṇa and others say about it?
Lying by itself is not adharma. The intent behind the lie is important in determining whether it's dharma or adharma. In a life-threatening situation to protect oneself, one can lie or just remain silent (i.e., not speak the truth).
In Karṇa Parva of the Mahābhārata, Kṛṣṇa, speaking on truth, dharma, keeping one's vows etc., narrates the following story to Arjuna.
There lived an ascetic by the name Kauśika who's taken a vow to always speak the truth (no matter what). He quickly became famous due to that fact. One day, a group of people, being chased by robbers, ran from the front of his house into the woods. When robbers inquired the whereabouts of those people, Kauśika being very truthful, points them exactly which way the people went. The robbers then proceed in that direction, search out all those people and end up robbing and killing them. Since Kauśika was partly responsible for the death of the innocent people at the hands of cruel robbers, he goes to hell.
In consequence of that great sin consisting in the words spoken, Kauśika, ignorant of the subtilities of morality, fell into a grievous hell, even as a foolish man, of little knowledge, and unacquainted with the distinctions of morality, falleth into painful hell by not having asked persons of age for the solution of his doubts.
There are other examples like Yudhiṣṭhira lying in the battlefield to deceive Droṇa who seemed invincible when he was launching an array of weapons on the Pāṇḍava army.
And in Śānti-parva, responding to Yudhiṣṭhira's query: "How should a person, who wishes to follow virtue, act?", Bhīṣma says:
यस्मिन्यथा वर्तते यो मनुष्य: स्तस्मिंस्तथा वर्तितव्यं स धर्मः ।
मायाचारो मायया वर्तितव्य; साध्वाचार साधुना प्रत्युदय ।।
yasmin yathā vartate yo manuṣyas; tasmiṃs tathā vartitavyaṃ sa dharmaḥ ।
māyācāro māyayā vartitavyaḥ; sādhvācāraḥ sādhunā pratyudeyaḥ ।।
One should treat another as the latter does to him. A deceitful person should be thwarted with deceit, while an honest man should be treated with honesty.
In Rāmāyaṇa too there's an instance where Rāma tells Daśaratha's minister Sumantra to lie should the king question him later why he'd ignored his order to stop the chariot.
Daśaratha exclaimed saying "Stop!" while Rāma called out "Go on, proceed!" (in that way) Sumantra's mind became confused, as in between two (opposing) whirl pools.
Rāma said to him: "You can say to the king that you did not hear (his call), even when scolded (later). Seeing their grief for a long time is quite unbearable."
All the above examples suggest that it's alright to lie sometimes to fulfill a bigger, dhārmic objective.
But the majority of time, one should follow dharma and satya. Manu defines the ten characteristics of dharma as follows. Truth (satya) is also one of them.
धृतिः क्षमा दमोऽस्तेयं शौचमिन्द्रियनिग्रहः ।
धीर्विद्या सत्यमक्रोधो दशकं धर्मलक्षणम् ॥ ९२ ॥
dhṛtiḥ kṣamā damo'steyaṃ śaucamindriyanigrahaḥ |
dhīrvidyā satyamakrodho daśakaṃ dharmalakṣaṇam || 92 ||
(1) Steadiness (2) Forgiveness, (3) Self-control, (4) Abstention from unrighteous appropriation, (5) Purity, (6) Control of the Sense-organs, (7) Discrimination, (8) Knowledge, (9) Truthfulness, and (10) Absence of anger,—these are the ten-fold forms of duty. — [Manu-smṛti 6.92]
Taittirīya Upaniṣad (1.11) also says:
सत्यं वद । धर्मं चर ॥ २ ॥
satyaṃ vada | dharmaṃ cara || 2 ||
Speak the true. Follow Dharma.