Lawrence appears in The Price Of Flesh as the Lich in the black swamp.
He will first show up while the MC is dreaming if/when their sanity drops below 50.
He can act as a guide for certain endings in Mason's route.
He is the main focus of one of the three secret achievements, SACRIFICE.
To get the sacrifice achievement, you have to complete the 'You Changed' ending while having 0 total deaths in your game data.
Meaning, you will most likely have to wipe your entire save because you really want the special CG that comes with the achievement and then to see said CG, you'll have to essentially 100% the game again.
So frustrating and dope.
Upon getting the ending with no deaths on your save, The Lich will comment on how you've never tasted death, how you were made for him, came straight to him... He says you'll be his forever and you unlock the achievement.
The CG you unlock depicts a seemingly older Lawrence beckoning the viewer into The River, his reflection in the water is the Lich.