I thought I would post a response I got from JMP Technical Support on setting the random seed.
"To generate reproducible results from Latent Class Analysis in Text Explorer, you must set the random seed before each using the Random Reset() JSL function.
Here is an example using the Pet Survey sample data that fits the LCA five times, with reseting the random seed before each. All 5 LCA results should be identical."
dt = open("$SAMPLE_DATA/Pet Survey.jmp");
te= Text Explorer(
Text Columns( :Survey Response ),
Set Regex( Library( "Words" ) ),
Language( "English" ),
);
for(i=1, i<=5, i++, //run LCA five times
RandomReset(123); //set the random seed before each
lca=te<< Latent Class Analysis(
Number of Clusters( 5 ),
Maximum Number of Terms( 143 ),
Minimum Term Frequency( 2 )
));