Is one allowed to lie in a case where telling the truth will cause great discomfort to the person he is speaking to?
Under such circumstances, it would be permitted to lie, and this is included in the general heter of darchei shalom. It is also required to avoid the prohibition of ona’as devarim (causing the other person distress).
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 Shavuos30b, 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 – andShulchan 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 (SeeChelkas 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 somebody is generally an issue of Shalom and permits a lie. Although not every instance of personal discomfort is sufficient for this to apply, we find further that it is permitted to lie in order to save oneself from shame (Rambam, Gezeilah 14:13, and commentary of Kesef Mishnah), and the same will apply to saving someone from being hurt.