  Lackadaisical quantum walk (LQW) is a quantum analog of a classical lazy
walk, where each vertex has a self-loop of weight $l$. For a regular
$\sqrt{N}\times\sqrt{N}$ 2D grid LQW can find a single marked vertex with
$O(1)$ probability in $O(\sqrt{N\log N})$ steps using $l = d/N$, where $d$ is
the degree of the vertices of the grid. For multiple marked vertices, however,
$l = d/N$ is not optimal as the success probability decreases with the increase
of the number of marked vertices. In this paper, we numerically study search by
LQW for different types of 2D grids -- triangular, rectangular and honeycomb --
with multiple marked vertices. We show that in all cases the weight $l = m\cdot
d/N$, where $m$ is the number of marked vertices, still leads to $O(1)$ success
probability.
