[7] Lau has published articles in journals such as Tehumin, and edited a book of his father's responsa titled Yichil Yisrael.

Dov Lior, the administering rabbi, asserted that Lau brought papers with answers to previous tests into the examination room.

[10] In his first week in office as Chief Rabbi of Israel, Lau referred to African-Americans who play basketball on Israeli teams as kushim.

[12] In 2018, Lau was accused of trying to appoint his brother-in-law, Mordechai Ralbag, as a replacement for a rabbinical judge who was investigating corruption involving hekdeshot (Haredi non-profit property trusts).

[15] In August 2019, Lau instructed the chevra kadisha to delay the burial in Jerusalem of the mother of an American Haredi man, Yisrael Meir Kin, until he agreed to give his wife a get (religious writ of divorce).

[17] He said that the divorce papers had been filed ten years earlier at a religious court in Monsey, New York, and Lau, who was related to his wife, had taken sides in the case.

[17] Lau's office responded to Kin's statements, saying that the chief rabbi was not aware of the family relation while dealing with the case,[17] and that they were sorry that Kin, who had denied his wife a get "for more than 15 years", was "continuing his refusal despite the agreements reached ... [Lau] will continue his unwavering war on the phenomenon of get-refusal, and "will do everything he can, including [imposing] the most severe sanctions, to end any case of get-refusal that may develop".

[20] In December 2021, Lau was criticised for attending the shiva of prominent Haredi author Chaim Walder, who had committed suicide amidst allegations of being involved in sexual abuse against minors and married women.

Natan Slifkin wrote in a blogpost By honoring the family with a visit while not making any statement about Walder, this lends support to the 'persecuted tzaddik (righteous one)' narrative.

[21] On 17 December 2023, in the midst of Israel's response to a Hamas-led surprise attack which left 1200 Israelis dead, it was reported that two women were killed by an IDF sniper in the courtyard of a Catholic church in Gaza.

Pope Francis, responding to this incident which occurred in the context of tens of thousands of other Palestinian deaths at the hands of the IDF, said "Some are saying, 'This is terrorism and war'.