Use code:

import javafx.application.Application;
import javafx.beans.property.SimpleBooleanProperty;
import javafx.beans.value.ObservableValue;
import javafx.event.ActionEvent;
import javafx.event.EventHandler;
import javafx.scene.Scene;
import javafx.scene.control.Button;
import javafx.scene.control.ListView;
import javafx.scene.control.cell.CheckBoxListCell;
import javafx.scene.layout.VBox;
import javafx.stage.Stage;
import javafx.util.Callback;
import javafx.util.StringConverter;

public class Main extends Application {

    public static void main(String[] args) {
        launch(args);
    }

    @Override
    public void start(Stage stage) throws Exception {
        VBox vb = new VBox();

        final ListView lv = new ListView();
        lv.getItems().addAll(new DataItem(), new DataItem(), new DataItem());

        Button b = new Button("Press me");
        b.setOnAction(new EventHandler<ActionEvent>(){

            public void handle(ActionEvent t) {
                Callback<DataItem, ObservableValue<Boolean>> callback1 = new Callback<DataItem, ObservableValue<Boolean>>() {

                                public ObservableValue<Boolean> call(final DataItem p) {
                                    return p.someData;
                                }
                            };
                lv.setCellFactory(CheckBoxListCell.forListView(callback1, new CellCustomStringConverter()));
            }
        });

        vb.getChildren().addAll(lv, b);

        Scene scene = new Scene(vb, 300, 300);
        stage.setScene(scene);
        stage.show();
    }

    class DataItem {
        public ObservableValue<Boolean> someData = new SimpleBooleanProperty(true);
    }

    public class CellCustomStringConverter extends StringConverter {

        public static final String TO_STRING_PREFIX = "tsc ";
        public static final String FROM_STRING_PREFIX = "fsc ";

        @Override
        public String toString(Object t) {
            System.out.println("Called to string");
            return TO_STRING_PREFIX + t != null ? t.toString() : "null";
        }

        @Override
        public Object fromString(String string) {
            System.out.println("called from string");
            return null;
        }
    }
}

When I Press button, I see output:
Called to string
Called to string
Called to string
Called to string

But I don't see "tsc " in the beginning of list items, when checkbox appears.