Why did Lew Wallace arrive so late?

Was Lew Wallace running away before his division entered the Battle of Shiloh?

No; he was guarding the northern approach, then lost time because Grant's missing written order was interpreted differently and his division had to change route.

Lew Wallace's division initially guarded a position north of Pittsburg Landing against Confederate cavalry. The written order sent from Grant's headquarters is lost, and Wallace and Grant later disagreed about what route it required. Wallace marched one way, was redirected by another staff officer, and ultimately covered about fourteen miles before arriving around 6:30 p.m. The starting distance remains uncertain in this account, but the countermarch explains why his division took so long to arrive.