I can only insert matrix without the stroke.
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if you want to draw this type of matrix using LyX's GUI (and not using ERT) you must do it with array and not pmatrix. In LyX: 1) enter math mode (via ctrl+M or ctrl+shift+M), 2) press Alt+M ( to add the parentheses, 3) type \array then space.
Now you should see the array menu at the bottom of the screen, there you can add rows and columns to the array.
After formatting the array to the desired size, right click on the column positioned to the left of the vertical bar you want to add, and press Add Line to Right.
Udi Fogiel
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nicematrix. – projetmbc Nov 21 '22 at 19:53