is it muttar to lie to avoid an uncomfortable situation?
e.g. you want to discontinue a business relationship (piano teacher or tutor etc..)& you don’t want to say that it’s because your dissatisfied with them u’kidomeh…
It is permitted to lie for the sake of not hurting the teacher’s feelings. However, not every case of discomfort would be sufficient to permit a lie.
Sources: The essential prohibition of lying, of which the Torah states that one must distance oneself from falsehood, applies specifically to lying in beis din (see Shavuos 30b, 31a). Although it is certainly unworthy practice to lie even outside of beis din, Chazal permit the practice for a number of purposes, the most prominent of which is for the sake of peace (Yevamos 65b). Concerning how a person should “dance before the bride,” Beis Shammai state that one should tell the truth, whereas Beis Hillel – and Shulchan Aruch (Even Ha’Ezer 65:1) write that one should praise her beauty irrespective of the truth. Ritva explains that this is an extension of the general permit of darchei shalom.
Although several authorities write that this is permitted only when the lie is not an outright lie – the “beauty” of the bride can be interpreted in various ways (See Chelkas Mechokek, Beis Shmuel, Prisha, Taz and Aruch Hashulchan), we find an explicit Gemara that permits lying to raise the spirits of the destitute (Nedarim 50b).
In the case of the question, it would seem that the general cause of Shalom is sufficient to permit the lie — avoiding hurting a teacher’s feelings is certainly an issue of Shalom and permits a lie. However, not every instance of personal discomfort is sufficient for this permit to apply. However, it is permitted to lie in order to save oneself from shame (Rambam, Gezeilah 14:13, and commentary of Kesef Mishnah).