I understand there’s a Heter to shave on Friday if Lag Ba’Omer falls out on Sunday. Does the same apply if Rosh Chodesh falls out on Sunday (like this year)?
The Mishnah Berurah explains that for those who keep the “first half” of the Omer period, there is no heiter (permission) to take a haircut on Rosh Chodesh, and the same will apply on Friday before Rosh Chodesh (493:14).
Concerning shaving, the majority of poskim do not make a distinction between shaving and taking a haircut, and therefore the same will apply to shaving on Friday. See, for instance, Iggros Moshe, Orach Chaim 4:102, and others.
However, there are some authorities who are more lenient concerning shaving than concerning a haircut, on account of their different natures — a haircut is something “special,” whereas many shave daily. For this reason, there are some who shave in honor of the Shabbos, even during the Sefirah period.
Yet, the common custom, and the opinion of most authorities, is to refrain from shaving during the Sefirah period (until Lag Ba-Omer), and this applies even on Rosh Chodesh, and on the Friday before it.