Crossunder - the engine failure 'on takeoff' could be out of an airport on an island, Male, Maldives. Straight ahead would be ok, no obstacles.
Straight ahead, is okay, provided obstacles are studied within the are as dictated by norms laid down for obstacle clearances/establishing an emergency turn.
What are your company's 'rules/norms' for calculating obstacle clearances regarding an 'engine failure on a twin'?
Bob ... wouldn't happen to be Lt. Col. Hammond?