Most people can't read a Torah scroll. So what are we looking at?
A scroll has no vowels and no punctuation, and many in the room could not read it. Yet the rule in Tractate Soferim says it is a mitzvah for all men and women to see the writing, to bow, and to say the line. The rule is about seeing the writing.
The Ramban (Rabbi Moshe ben Nachman, a leading medieval Torah commentator) links this to a verse in Devarim: "Cursed is the one who does not uphold the words of this Torah." The Yerushalmi (the Jerusalem Talmud, the Gemara of the Land of Israel) plays on the word "uphold" and asks whether a Torah can fall. One rabbi there says it is about the chazzan, the synagogue official who handled the scrolls. Ramban reads this as a chazzan who does not stand the scrolls up properly, so they fall.
Then Ramban gives his own thought: "It seems to me" the verse also means a chazzan who does not lift the scroll to show its writing, as Soferim describes. That is a possibility he offers. His main reading is about people who deny that the Torah's commands are true, not people who break one.
Later books say what the looking is for. The Mishnah Berurah says it is good to look at the letters until you could read them, because the Kabbalists (teachers of Jewish mysticism) wrote that this draws a great light onto a person. The Arukh HaShulchan (a code of Jewish law from around 1900) says the same and adds "if he is worthy of it."
So the sources agree on what to do and are less direct about why seeing matters. The reasons they give are respect for the scroll and the idea that the sight of the letters does something to a person. That second reason is a claim from mystics, and whether it speaks to you is up to you.
Tractate Soferim 14:14,Ramban on Devarim 27:26,Mishnah Berurah 134:11,Arukh HaShulchan, Orach Chaim 134:3Why does my shul lift the Torah after the reading and my friend's before?
Both orders are old, and the books say so openly. The Shulchan Aruch (the main code of Jewish law) describes the lifting before it gets to the laws of the Torah reading. The Mishnah Berurah (a standard commentary on it, written around 1900) explains why: that is the Sephardic custom, to lift before the reading. Then it points to the Rema, whose notes add Ashkenazi customs: our custom is to lift after the reading.
The Arukh HaShulchan (a code of Jewish law from around 1900) says the same. In his words, we lift after the reading and the Sephardim lift before it, and he adds that the Sephardic order is what Tractate Soferim implies.
The Kaf HaChaim (a long commentary on the Shulchan Aruch, written in Jerusalem and printed from 1910 to 1933) gives a reason for the Ashkenazi order, which he takes from earlier books. He calls it a proper custom, because ordinary people think that seeing the Torah matters more than reading it. So that they will stay, the reading comes first and the showing of the writing comes after.
The note printed in this siddur places the lifting after the reading, so that is the order this page follows.
The Kaf HaChaim also quotes a book called Shaarei Yerushalayim, which says that in the Land of Israel even Ashkenazim lifted the Torah before the reading, and not as the Rema describes. So the split is not only Ashkenazi against Sephardi. It follows the place and the community.
Neither order is a mistake. Both are written down, with reasons. The mitzvah to see the writing is the same either way.
Mishnah Berurah 134:8,Shulchan Aruch, Orach Chaim 134:2 (Rema),Arukh HaShulchan, Orach Chaim 134:3,Kaf HaChaim, Orach Chaim 134:17The line we say sounds like it is from the Torah. Where is it?
Look at the first line again: "And this is the Torah that Moshe set before the people of Israel, at Hashem's command, through Moshe." It sounds like a verse. It is not one.
The Arukh HaShulchan (a code of Jewish law from around 1900) points this out. He calls it a wonder that we say it and that siddurim print it, and then he gives problems. First, it is not a verse anywhere. "And this is the Torah" is in Devarim 4:44. "At Hashem's command, through Moshe" is the end of a verse in Bamidbar, in the passage about when the Jews camped and when they traveled in the desert.
Second, he says Tractate Soferim does not have it this way either. Soferim gives the line as it is in Devarim, and it stops at "before the people of Israel."
There is another difference. Rashi (the main commentator on the Torah) says that in Devarim 4:44, "this Torah" means what Moshe is about to set out after this passage. In the verse, "this" points forward, to what he is about to teach. In shul, it points at the scroll in front of you.
None of these sources says who joined the two pieces together or why. What they do show is that the longer wording is printed in siddurim, while Soferim stops at the end of the Devarim sentence and then gives a line from Tehillim, "The Torah of Hashem is perfect."
Arukh HaShulchan, Orach Chaim 134:3,Devarim 4:44,Bamidbar 9:23,Tractate Soferim 14:14,Rashi on Devarim 4:44