1)
Why does it say that he is going from Beis Lechem... and to Beis Lechem?
1.
Malbim: I am from there, and that is my destination, but I cannot reach there during the day.
2)
Was he really going to Beis Hashem (the Mishkan in Shilo)?
1.
Radak #1: Yes. He was from Har Efrayim, and Shilo was in Efrayim (Yehoshua 16:6).
2.
Radak #2: He was going there to offer a Korban or pray; he did not live there. He said that he is going to Beis Hashem, so the old man will be happy to host him.
3.
Malbim: He said this lest the man think that he serves Pesel Michah, which was in Har Efrayim.