  As in the case of minimal surfaces in the Euclidean 3-space, the reflection
principle for maximal surfaces in the Lorentz-Minkowski 3-space asserts that if
a maximal surface has a spacelike line segment $L$, the surface is invariant
under the $180^\circ$-rotation with respect to $L$. However, such a reflection
property does not hold for lightlike line segments on the boundaries of maximal
surfaces in general.
  In this paper, we show some kind of reflection principle for lightlike line
segments on the boundaries of maximal surfaces when lightlike line segments are
connecting shrinking singularities. As an application, we construct various
examples of periodic maximal surfaces with lightlike lines from tessellations
of $\mathbb{R}^2$.
