So Sherlock deduced that Faith is suicidal because she’s walking around with a cane, no coat on, a gun, and no plan to get home. Which we are then, on camera, explicitly told parallels ASIP John Watson.
So he comes up with a reason to have Faith by his side so he can help her through her danger night.
Which is not at all dissimilar to having John tag along to angelo’s, go on a chase, and spark a joy for life again.
Sherlock knew. When he summoned John across London on that fateful first night “just to send a text”, it wasn’t because he was being a prat, he was trying to save John’s life.