The Subjunctive Mood is used in adverbial clauses of purpose. When a clause of purpose is introduced by the conjunctions that, so that, in order that, we find the analytical subjunctive with the mood auxiliary may (might) if the principal clause refers to the present or future; if the principal clause refers to the past, only the form might is used.

As has already been, stated, the mood auxiliary may (might) retains in this case a shade of modality.

She opens (will open) the window that she may (might) get a breath of fresh air.
She opened the window that she might get a breath of fresh air.
Order a conveyance to be at the door to-morrow evening, rather earlier than is absolutely necessary, in order that we may be in good time. (Dickens)
Mr. Micawber impressed the names of streets upon me that I might find my way back easily. (Dickens)
Не got up, cautiously, so that he might not wake the sleeping boy. (Cronin)

Occasionally the mood auxiliary should is used.

I made shorthand notes of all that she said, however, so that there should be no possibility of a mistake. (Conan Doyle)

If a clause of purpose is introduced by lest the mood auxiliary should (for all persons) is generally used.

Lest has a negative meaning.
She opens (opened, will open) the window lest it should be stuffy in the room.
She… looked steadily at her coffee lest she also should begin to cry, as Anna was doing already. (Eliot)