What are the connotations of "le'Shochni be'Socham"?
Rashi and Rashbam: It means that Hashem took Yisrael out of Egypt with the intention 1 of dwelling in their midst.
Ramban #1: It means that when Hashem dwells in their midst, 2 they will know that He is their G-d, and believe that He took them out of Egypt.
And the 'Lamed' in "Leshochni" means 'in order to ... '.
This appears to conform to the explanation of Targum Onkelos and Targum Yonasan.
Ramban (citing the Ibn Ezra): As Hashem told Moshe at the Burning Bush in Sh'mos, 3:12. Because, according to Kabalah, the Shechinah dwelling in Yisrael is more for Hashem's sake than for Yisrael's, as is implied in Yeshayah, 49:3, Yehoshu'a, 7:9, and even more blatantly, in Tehilim, 132:13, 14 (See R. Chavel's footnotes).