Difference between Christian God and Islamic Allah is: Allah is not a father.
So ‘name of the father’ rhetoric does not work on a Muslim. Lacanians may need to consider that.
I have a quick solution for you. Like Lacan said ‘these people’ cannot be analysed. You can add Muslims to that list.
If they are not already in it of course.
If you are going to convert psychoanalysis into some kind of conversion therapy it is on your own responsibility. Not Other’s responsibility.