This might be too late for you but I hope it helps someone since it took me a while to figure out.
To run Latin Square in JMP, you must have Row, Column, Treatment and the Y-response.
You must set your data type correctly for all of the variables (Row, Column and Treatment). You must change the column information, double click on the column: Data type as Character Modeling type as Nominal. If your x variables are in numbers/continuous it will run as regression.
Then Analyze/ Fit model/ put Y in Y and all the Row, Column and Treatment under "Construct Model Effects", keep all others as default. Run
Click on Response Y red triangle/ Estimates/Multiple comparisons to get the LSD for your treatment. If you use student's t, then check it. Click on red triangle of Student's t to get All pairwise differences connecting letters.
Kieu