Is it true that speaking in the lavatory necessitates the angel's entry to record the word, and is considered a harm to him?

Speaking unnecessarily while relieving oneself is prohibited. As for the recording angels, they do not leave a person in any place he might be, because their function is to monitor his actions and words, in fulfillment of Allah's saying: "He utters no word except that with him is an observer, ready [to record]."

A weak hadith has been reported from Ibn 'Umar that the Prophet, peace and blessings be upon him, said: "Beware of nudity, for there are with you those who never leave you, except at the time of defecation and when a man goes to his wife. So be shy of them and honor them."

Therefore, the prohibition of speaking in the toilet is not out of fear of the angel entering, but rather to keep the remembrance of Allah and similar things pure from that place.