We have now had a little of Lorca's back story and we can perhaps see that his experiences have filled him with pain, hate, guilt and implacable resolve to win at all costs.
Burnham has also lost much and is pained and and feeling guilty and both are trying to do penance for their shame and guilt, however Burnham despite her Vulcan upbringing is in possession of much more humanity and compassion than Lorca.
I believe one of the key plot points going forward is that she should talk him down off his self imposed ledge to become a more reasonable leader. To remind him that for a victory to mean anything they must remain true to their ideals so that if they emerge on the other side of the conflict they can do so with honour.
One of the lines from Ender's Game springs to mind "The way we win matters" and I think that it is Burnhams place to remind Lorca of that.