The details on how to maneuver around the Display Trees of the output, is documented in the Scripting Guide. But basically, the Report Output from the various platforms is a structure of display objects that can be referenced by name and/or location and to have messages passed to them. Below is a Fit Model close to what you are asking for, that runs the model and then goes to the Least Squares Means Table of your choice and tells it to Create Data Table.
Names Default To Here( 1 );
dt = Open( "$SAMPLE_DATA/big class.jmp" );
fm = dt << Fit Model(
Y( :weight ),
Effects( :age, :sex ),
Personality( Standard Least Squares ),
Emphasis( Effect Leverage ),
Run( Residuals( 1 ) )
);
Report( fm )["age"]["Least Squares Means Table"][Table Box( 1 )] << make data table;
Jim