How to replicate this 2-1 layout in JavaFX?

I've looked into all of the layout options in the docs, and I am not allowed to use FXML. I don't understand where to start with configuring the 3 containers in the scene.

There are many ways you can do this; probably the most immediate is to put the two panes on the left in a VBox, and then use a BorderPane, with the VBox on the left and the "CCTV" pane in the center. This looks like:

import javafx.application.Application;
import javafx.geometry.Insets;
import javafx.scene.Scene;
import javafx.scene.control.Label;
import javafx.scene.layout.BorderPane;
import javafx.scene.layout.Pane;
import javafx.scene.layout.Priority;
import javafx.scene.layout.VBox;
import javafx.stage.Stage;
public class LayoutExample extends Application {
@Override
public void start(Stage primaryStage) throws Exception {
Pane lighting = new Pane(); 
lighting.getChildren().add(new Label("Lighting"));
Pane heating = new Pane();
heating.getChildren().add(new Label("Heating"));
Pane cctv = new Pane();
cctv.getChildren().add(new Label("CCTV"));
lighting.getStyleClass().add("control-pane");
heating.getStyleClass().add("control-pane");
cctv.getStyleClass().add("control-pane");
BorderPane root = new BorderPane() ;
VBox left = new VBox();
left.getChildren().add(lighting);
left.getChildren().add(heating);
// expand both panes in left to full width of vbox:
left.setFillWidth(true);
// add vertical space between panes:
left.setSpacing(5);
// allocate extra vertical space equally to both panes in left:
VBox.setVgrow(lighting, Priority.ALWAYS);
VBox.setVgrow(heating, Priority.ALWAYS);
root.setLeft(left);
root.setCenter(cctv);
// Add a left margin to the center pane to give it some space:
BorderPane.setMargin(cctv, new Insets(0, 0, 0, 10));
Scene scene = new Scene(root);
scene.getStylesheets().add(getClass().getResource("layout-style.css").toExternalForm());
primaryStage.setScene(scene);
primaryStage.setWidth(800);
primaryStage.setHeight(640);
primaryStage.show();
}
public static void main(String[] args) {
Application.launch(args);
}
}

This CSS isn't quite right, but gives you an idea how to add the borders:

<!-- language: css -->

.control-pane {
-fx-background-color: -fx-body-color, -fx-outer-border, -fx-body-color ;
-fx-background-insets: 0, 1, 2 ;
-fx-background-radius: 0, 1, 0 ;
-fx-padding: 3 ;
/** Just to demo empty boxes: **/
-fx-min-width: 300px ;
-fx-min-height: 300px ;
}

This looks like:

You could also use a HBox as the root, and set the hgrow on each to prioritize extra horizontal space on the CCTV pane. Or use a GridPane, and set the row span of the CCTV pane to 2. There are probably many other ways to do this.