  The concept of lackadaisical quantum walk -- quantum walk with self loops --
was first introduced for discrete-time quantum walk on one-dimensional line.
Later it was successfully applied to improve the running time of the spacial
search on two-dimensional grid.
  In this paper we study search by lackadaisical quantum walk on the
two-dimensional grid with multiple marked vertices. First, we show that the
lackadaisical quantum walk, similarly to the regular (non-lackadaisical)
quantum walk, has exceptional configuration, i.e. placements of marked vertices
for which the walk has no speed-up over the classical exhaustive search. Next,
we demonstrate that the weight of the self-loop suggested in the previous
papers is not optimal for multiple marked vertices. And, last, we show how to
adjust the weight of the self-loop to overcome the aforementioned problem.
