What is the Muslim term/practice/belief that states that it is ok to lie to and misinform non-believers?

It is called TAQIYYA. There is also something known as Kitman.

In short: Taqiyya - Saying something that isn't true.

Kitman - Lying by omission.

Taqiyya (تقي), also spelt Taqiya / Tuqya / Taqqiyah, is known as lying for Islam. While many claim it is only practiced within Shi'ite Islam, it is also mentioned in many Sunni hadith and by many of their Islamic scholars.

Despite the overtly cruel, harsh and intolerant Qur'anic views towards the 'others,' namely Jews and Christians, there are injunctions in the Qur'an that enable the Islamic community to disguise, play down, and, when necessary, deny both the intensity and validity of these anti-Semitic and anti-Christian teachings of its religious system.

[Takiyya] permeates almost all the activities and dealings of Muslims within non-Muslim societies...

Takiyya means "caution, fear, or disguise." It permits the suspension, as the need arises, of almost any or all religious requirements--including a total denial of faith--when fearing threat, injury or compulsion of any kind in a non-Muslim society, or even in a Muslim society.

Kitman

Kitman is close to Taqqiya but rather than outright dissimulation, it consists in telling only part of the truth, with “mental reservation” justifying the omission of the rest (adjustment, deception etc, anything short of a full-blown lie).

For example when a Muslim maintains that “jihad” really means “a spiritual struggle” and fails to add that this particular definition is a recent invention in Islam (little more than a century old), he misleads by holding back the true violent nature of jihad, and is therefore practicing “kitman.”

Another example would be the insistence of a Muslim apologist that “of course” there is the freedom of conscience in Islam, followed by quoting the Qur’anic verse “There shall be no compulsion in religion.” The impression given is false, for there has been no mention of the Islamic doctrine of abrogation, or naskh.

Muslims are allowed to lie about their religion if it would put them in danger, as it might in a non-Muslim land. This is the normal use of Taqiyya. However, there are a number of hadith that show that lying is permissible, if it is against an enemy (and most non-Muslims are considered enemies)

One hadith is a good example. Ka’b bin Al-Ashraf maligned Muhammed in some way (probably by speaking against him). Muhammad had him murdered.

From Bukhari vol.5 book 59: "Narrated Jabin bin ‘Abdullah : Allah’s Apostle said, ‘Who is willing to kill Ka’b bin Al-Ashraf who has hurt Allah and His Apostle?’ Thereupon Muhammad bin Maslama got up saying, ‘O Allah’s Apostle! Would you like that I kill him?’ The Prophet said, ‘Yes.’ Muhammad bin Maslama said, ‘Then allow me to say a (false) thing (i.e. to deceive Ka’b).’ The Prophet said, ‘You may say it.’

And it was done (for more, see the link)

Taqiyya, as demonstrated below.

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