A supplicatory use cannot be recognized merely by the appearance of lā. The speaker’s humility, the aim of the plea, and the relationship with the addressee supply the evidence.
اللَّهُمَّ لَا تَحْرِمْنَا رَحْمَتَكَ
O Allah, do not deprive us of Your mercy.
This is a supplication, not an order issued to God. It illustrates the direction of an imploring request.
The textbook’s phrase “fa-lā tushmit biya al-aʿdāʾ” likewise has prohibitive grammar yet functions as an appeal. Literal and supplicatory uses may both involve refraining from something, but the social stance differs.