The Cabbibo-favored decay Lambda thorn c -> Xi 0K thorn pi 0 is studied for the first time using 6.1 fb-1 of e thorn e- collision data at center-of-mass energies between 4.600 and 4.840 GeV, collected with the BESIII detector at the BEPCII collider. With a double-tag method, the branching fraction of the three-body decay Lambda thorn c -> Xi 0K thorn pi 0 is measured to be o7.79 1.46 0.95 thorn x 10-3, where the first and second uncertainties are statistical and systematic, respectively. The branching fraction of the two-body decay Lambda thorn c -> Xi o1530 thorn 0K thorn is o5.99 1.04 0.32 thorn x 10-3, which is consistent with the previous result of o5.02 0.99 0.31 thorn x 10-3. In addition, the upper limit on the branching fraction of the doubly Cabbibo-suppressed decay Lambda thorn c -> nK thorn pi 0 is 7.1 x 10-4 at the 90% confidence level. The upper limits on the branching fractions of Lambda thorn c -> sigma 0K thorn pi 0 and Lambda K thorn pi 0 are also determined to be 1.8 x 10-3 and 2.0 x 10-3, respectively