How to create a structured mesh on the L-shape domain?

mesh
2

You should consider using external meshing tools such as gmsh, which has several tutorials.
Minimal geo file with upper left quadrant removed:

//+
SetFactory("OpenCASCADE");
Rectangle(1) = {0, 0, 0, 1, 0.5, 0};
Rectangle(2) = {0.5, 0.5, 0, 0.5, 0.5, 0};

Transfinite Surface{1} = {1,2,3,4};
Transfinite Surface{2} = {5,6,7,8};
Physical Surface(1) = {1,2};