If boy reaches his thirteenth birthday during the Omer period, before Lag Ba’omer, is he allowed to take a haircut on that day in honor of the occasion?
This issue is subject to a dispute among the Halachic authorities. Some, including Rav Menashe Klein (New York, 1923-2011), in Mishneh Halachot (6:45), forbade taking a haircut during the Omer on the day one becomes a Bar Misva. Hacham Ovadia Yosef, however, in Hazon Ovadia – Hilchot Yom Tov (p. 266), disagrees, and allows a boy to take a haircut on the day he becomes a Bar Misva. However, he writes that it is preferable for the boy to take a haircut before his thirteenth birthday, because then is still regarded as a minor, and there is thus greater room for leniency. Therefore, if, for example, a boy becomes a Bar Misva on Friday, he should preferably take a haircut on Thursday, rather than wait until Friday.
The authorities also dispute the question of whether the Bar Misva boy’s father may take a haircut in honor of the occasion during the Omer. One view (mentioned in the work Halichot Shelomo) forbids the father from cutting his hair or shaving during the Omer in honor of his son’s Bar Misva, but others (Rav Yitzchak Liebes, Bet Abi 2:20) rule leniently. As the restrictions of the Omer period apply only as a Minhag (accepted custom), there is room to follow the lenient view, and thus those who permit a father to take a haircut and shave in honor of his son’s Bar Misva during the Omer have a basis for their practice.
Summary: A boy who becomes Bar Misva during the Omer period may take a haircut in honor of the occasion, though it is preferable for him to take a haircut before his thirteenth birthday, when he still regarded as a minor. There is room to allow the father to take a haircut in honor of the occasion, as well.