How can I check a box on a sublist of type LIST in a client script?

I'm not sure what you mean with "a sublist of type LIST", but would this work?

/**
 * @NApiVersion 2.0
 * @NScriptType ClientScript
 */

define([],
  function() {	

  function fieldChanged(context) {
    context.currentRecord.setCurrentSublistValue({sublistId: 'item', fieldId: 'checkboxField', value: true});
  } 
  return { fieldChanged: fieldChanged, };
});

serverWidget.SublistType tells you how to make a field in the list type sublist editable