Q. On a ta’anis, by Mincha, a guy spaced out and, forgetting that there is krias hatorah, said Hashem Sefasai Tiftach and Baruch ata Hashem (ie. he began SE). May/ should he stop, say lamdeini chukecha, listen to krias hatorah, and then daven together with everyone else? Or should he continue once he already started?

A. Horav Shlomo Miller’s Shlit’a opinion is that once one has started the amida and said the first words of the bracha he should continue with the rest. The reason is that it is improper and disrespectful to interrupt the address being said to the King of the Universe.
However, while one is slowly reciting the amida, he may stop between the brochos and listen quietly to the Krias Hatorah; while being careful not to stop and be mafsik a stretch longer that the time it would take to recite the complete amida. (Mishna Berura 65: 3, see also s.104). One may however, while they call another reader to the Torah, continue with the amida.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a