All the transmitters in this chain are reliable and belong to those relied upon by the authors of the Six Books, except for al-Ḥaḍramī ibn Lāḥiq; he is “acceptable,” as stated in al-Taqrīb, but Ibn Ḥajar also notes that he belongs to the sixth tier, meaning those for whom meeting a Companion has not been established. On that basis the ḥadith is considered interrupted. (1)

Al-Haythamī said (2/20): “It was narrated by Aḥmad, and its transmitters are deemed reliable.”

I add: the report is further strengthened by the supporting narration that he himself cites immediately afterwards in al-Majmaʿ: “From a shaykh of Mecca, of Quraysh, who said: A man found a louse in his garment and was about to throw it into the mosque. The Messenger of Allah (Allah bless him and grant him peace) said, ‘Do not do that; put it back in your garment until you leave the mosque.’” Aḥmad recorded it, and its transmitters are trustworthy, except that Muḥammad ibn Isḥāq reported it with an unbroken “ʿan-ʿanah” and he is known for hiding intermediaries (mudallis).

I have not, for the time being, located this narration in the Musnad.

(2) Lighting the mosque without extravagance is indicated by his ﷺ statement regarding Jerusalem: “Go to it and pray there; if you cannot go and pray there, then send oil so that its lamps may be lit.” This text has already been cited.

The ḥadith was related by Abū Dāwūd in these very words, and by Aḥmad and Ibn Mājah with a different wording that was quoted earlier along with its grading when discussing al-Masjid al-Aqṣā.