Lattice conditional independence (LCI) models (Anderson and Perlman, 1991. Statist. Probab. Lett. 12, 465-486; 1993 Ann. Statist. 21, 1318-1358) can be applied to the analysis of missing data problems with non-monotone missing patterns. Closed-form maximum likelihood estimates can always be obtained under the LCI models naturally determined by the observed data patterns. In practice, it is important to test the appropriateness of LCI models. In the present paper, we derive explicit likelihood ratio tests for testing LCI models based on a monotone subset of the observed data.