Lethe, and Lorca's motivations.

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Lorca has probably realised, that his command might be on somewhat wobbly feet, and so that seeming wobbliness has little to do with his ship, its crew, or the Klingons. There are many indications as to why. So, danger to his command manifests from outside the ship, not from within, and not because Lorca has his own issues.

On one hand, he likes Burnham, and her continued presence has given him a very good track record, especially with regard to getting the ship to jump multiple times, and making several missions successful. Essentially, winning. Burnham is like a good omen, or an amulet or talisman.

On the other hand, anyone he doesn't like, or which may potentially harm him, his command, or his ship, is put on a shuttle. Losses are inevitable during wartime.

On TNG, DS9, and Voyager, people usually survive a Starfleet shuttle trip. Sometimes, by only a hair's breadth, but still. But Discovery's track record of putting people on shuttles places the putting of Dr. Moriarty on a shuttle in TNG into what now is a very different context from back then.

Another problem is, that this young Starfleet apparently only accepts flawless people. The picture is different by TNG (Lt. Barclay).

I've noticed, that these apparently flawless people (Landry) do die on Star Trek: Discovery. Other Star Trek shows usually never show Starfleet officers of relative or low importance die, even if it's talked about. Granted, the the dead person is shown or talked about only after the death has occurred. And then an investigation happens. The difference is, that in Discovery, people are now shown on-screen, some of the viewers already root for even the minor characters, and then they die. Or maybe we have seen the comeback of redshirts in a different form.

I wouldn't see "Lethe" or every episode through the prism of trauma and other such afflictions.

Burnham's decisionmaking wrt the Klingons has, though, been informed by her trauma from her early childhood and the Klingon attack, but also the Vulcan drive to suppress her human emotions, which she's been unable to process properly for much of her life, especially when in a critical situation. The lack of war, and her posting on U.S.S. Shenzhou has shielded her from critical situations. The Battle of the Binary Stars was the first such occasion.

Whereas Lorca's conduct is not based on trauma, but survival instinct. Admiral Cornwell is also much too nosy, thinking the rescue mission to save Sarek as trivial. Strange that. For Lorca, Sarek is an important puzzle piece that keeps Burnham in order.