In previous years, we have discussed the disagreement among the Poskim whether the mourning customs of the Omer should be observed until the 33rd or 34th day of the Omer. Sephardic and Middle Eastern Jews follow the ruling of Maran Ha’Shulchan Aruch (Chapter 493) who writes that all mourning customs remain in effect until the morning of the 34th of the Omer. Ashkenazi Jews, however, rule leniently in this regard and cease observance of these mourning customs from the 33rd of the Omer. (There are other customs as well, especially according to the Mekubalim who abstain from taking haircuts until Erev Shavuot.)
Thus, on all other years, Sephardic Jews only allow haircuts on the morning of the 34th of the Omer. This year (5781), when Lag Ba’Omer (the 33rd of the Omer) falls out on Friday, Erev Shabbat, and the 34th of the Omer coincides with Shabbat, it would seem that Sephardic Jews should abstain from shaving or taking haircuts until after Shabbat (since it is certainly forbidden to do so on Shabbat due to the sanctity of Shabbat).
Nevertheless, Maran Ha’Shulchan Aruch writes: “It is customary not to take haircuts until the 33rd of the Omer, for it is then that they say the students of Rabbi Akiva ceased dying. One should not take a haircut until the morning of the 34th of the Omer, unless the 33rd of the Omer falls out on Erev Shabbat, in which case one may take a haircut then in honor of Shabbat.”
This means that although Sephardic Jews usually abstain from taking haircuts until the morning of the 34th of the Omer, on years like this when the 34th of the Omer falls on Shabbat, if we do not allow people to take a haircut on Friday, the 33rd of the Omer, they will enter Shabbat looking disheveled and only take a haircut after Shabbat. Thus, on years like this, even Sephardic Jews may shave and take a haircut on Friday, in honor of Shabbat.
The last time this occurred was in the year 5768 (2008) when Erev Pesach coincided with Shabbat and Lag Ba’Omer coincided with Friday, as it does this year. The next time this is slated to occur is in the year 5785 (2025) and then again in the year 5805 (2045). With Hashem’s help, Mashiach will have already arrived long before these dates at which point holidays will be established through witnesses before the Sanhedrin who will convene on the Temple Mount and as such, these dates are subject to change.
Maran Rabbeinu Ovadia Yosef zt”l writes (in his Chazon Ovadia- Yom Tov, page 267) that if one does not have enough time to do so on Friday, one may even shave and take a haircut on Thursday night. It is likewise permissible to hold a wedding for a groom who has not yet fulfilled the Mitzvah of having children on Thursday night, the night of the 33rd of the Omer, as Ashkenazim would on other years.
Summary: This year, when Lag Ba’Omer falls out on Friday, even Sephardic Jews may shave and take haircuts on Friday in honor of Shabbat. If one does not have enough time to do so on Friday, it is even permissible to so beginning from Thursday night. Regarding the other mourning customs, it is permissible to listen to music in any case on Lag Ba’Omer when we celebrate this joyful day and omit Tachanun.