  We determine all the Q-fundamental surfaces in $(p,1)$-lens spaces and
$(p,2)$-lens spaces with respect to natural triangulations with $p$ tetrahedra.
  For general $(p,q)$-lens spaces, we give an upper bound for elements of
vectors which represent Q-fundamental surfaces with no quadrilateral normal
disks disjoint from the core circles of lens spaces.
  We also give some examples of non-orientable closed surfaces which are
Q-fundamental surfaces with such quadrilateral normal disks.
