It　is　critical　to　accurately　extract　the　natural　frequencies　in　the　transverse　vibration　of　plates　using　the　classical　plate　theory　(CPT)　and　the　first　-order　shear　deformation　plate　theory　(FSDT).　The　moving　least　squares　(MLS)　based　numerical　manifold　method　(MLS-based　NMM)　in　conjunction　with　a　suitable　diagonally　lumped　mass　matrix　is　a　reasonable　choice　because　it　can　naturally　treat　plates　with　cutouts　and　easily　formulate　an　H2　regular　approximation　based　on　MLS　interpolation,　as　well　as　mitigate　shear　locking　issues　for　vibration　analysis　of　thin　plates　based　on　FSDT.　Moreover,　the　mass　lumping　techniques　involving　the　row　-sum　method,　the　diagonal　scaling　method,　and　the　mathematically　rigorous　manifold　-based　method　are　extended　and　derived　in　the　unified　framework　of　MLS-based　NMM　for　transverse　vibration　analysis　of　plates.　Furthermore,　the　positive　-definiteness　of　the　lumped　mass　matrix　(LMM)　generated　by　the　manifold　-based　mass　method　is　explained　in　MLS　settings,　and　the　row　-sum　method　is　proven　to　be　a　special　case　of　the　manifold　-based　method.　A　comprehensive　comparative　study　of　different　LMMs　is　performed　in　accordance　with　the　consistent　mass　matrix　(CMM)　on　extensive　numerical　benchmarks.　Numerical　results　demonstrate　the　convergence　properties　of　LMMs　compared　with　CMM　in　MLS-based　NMM　for　plate　vibration　based　on　CPT　and　FSDT.　It　can　be　observed　that　LMMs　yield　comparable　performance　compared　with　CMM.　The　row　-sum　method　obtains　accurate　results　in　most　cases　but　can　not　guarantee　the　positivity.　In　contrast,　the　manifold　method　can　guarantee　the　positive　-definiteness　of　LMM　and　is　more　accurate　than　the　diagonal　scaling　method　in　most　cases.