Your call.
Datasheet says Vo - Vi needs to be 3V or more.
7.4V - (diode drop) - 3V = 4.4V -(diode drop).
So with 1V diode - can't get 4V out:
7.4-1-3 = 3.4V
With schottky diode:
7.4 - 0.4 - 3 = 4V.
You may see 4V for a while when the LiPo is fully charged and sitting at 8.4V. (4.2V/cell)