Why should he lie on his left side?
Rashi: He will suffer pain and afflictions the number of days like the number of years that it is as if My Ru'ach pained me, for they angered Me. You will atone for their sin, for the punishments that I say to bring against them are harsh in your eyes.
Radak: This is another Os for Bnei Yisrael. People lie mostly on the left side. Therefore, He commanded him to sleep on it for the sin of Yisrael, for they are the majority.
Radak citing Rashi (6): Shomron (the capitol of Malchus Yisrael) was on the left of Eretz Yisrael - "v'Achosech ha'Gedolah Shomron? ha'Yosheves Al Smolech" (16:46). Therefore, he lies on the left to atone for its sin.
Malbim: This hints that the reason for the sin of Beis Yisrael (the 10 tribes) was the left side. Hashem's right represents miraculous conduct, in which "Yemin Hashem Osah Chayil" (Tehilim 118:16). The left represents natural conduct. Since He conducted the 10 tribes naturally, and did not do for them many signs and wonders, and did not constantly send Nevi'im to rebuke them 1 , they sinned with idolatry. [Lying on the left] advocated for Beis Yisrael!
Nevi'im were sent to rebuke kings, e.g. Achav, but we do not find that they went around rebuking the 10 tribes themselves. (PF)
How will lying on his left side atone for sin?
Radak: Lying on one side for a long time without switching to the other side, is very hard. This was a sign for them that the years that they did not serve Hashem, they served Goyim and suffered their harsh Avodah. All this lying was in a prophetic vision.