Look at the attached movie.

I've applied formatter, to make label to be longer (wider). and started to rotate. You may see, that if angle equal to +/-50 degrees, then labels look like corresponding to the neighbor tick. I've demonsrated it in the end, that zero label correspond to the first tick.

Code:

import java.util.Arrays;
import java.util.Comparator;
import java.util.Random;
import javafx.application.Application;
import javafx.collections.FXCollections;
import javafx.collections.ObservableList;
import javafx.scene.Scene;
import javafx.scene.chart.LineChart;
import javafx.scene.chart.NumberAxis;
import javafx.scene.chart.XYChart;
import javafx.scene.control.Slider;
import javafx.scene.layout.Pane;
import javafx.scene.layout.VBox;
import javafx.stage.Stage;
import javafx.util.StringConverter;

public class JavaCharts extends Application {
    
    public static void main(String[] args) {
        launch(args);
    }
    NumberAxis axis1 = new NumberAxis(0, 100, 10);
    NumberAxis axis2 = new NumberAxis(0, 100, 10);
    LineChart testedLineChart = new LineChart(axis1, axis2);
    VBox vb = new VBox();
    
    @Override
    public void start(Stage stage) throws Exception {
        testedLineChart.setTitle("LineChart");
        testedLineChart.setStyle("-fx-border-color: darkgray;");
        
        ObservableList list = FXCollections.observableArrayList();
        int max = 100;
        int min = 30;
        
        for (int i = 0; i < 30; i++) {
            XYChart.Data newData = new XYChart.Data();
            newData.setXValue(new Random().nextDouble() * (max - min) + min);
            newData.setYValue(new Random().nextDouble() * (max - min) + min);
            list.add(newData);
        }
        Object[] array = list.toArray();
        Arrays.sort(array, new Comparator() {
            
            @Override
            public int compare(Object t, Object t1) {
                return (int) Math.round(((Double) ((XYChart.Data) t).getXValue()) - ((Double) ((XYChart.Data) t1).getXValue()));
            }
        });
        
        XYChart.Series serie = new XYChart.Series("serie", FXCollections.observableArrayList(array));
        
        testedLineChart.getData().add(serie);
        testedLineChart.setAlternativeColumnFillVisible(true);
        testedLineChart.setAlternativeRowFillVisible(true);
        
        Pane pane = new Pane();
        pane.setPrefSize(600, 600);
        
        axis2.setTickLabelFormatter(new ChartsLabelFormatter<Number>());
        
        Slider slider = new Slider(-60, 60, 0);
        slider.valueProperty().bindBidirectional(axis2.tickLabelRotationProperty());
        
        pane.setPrefSize(600, 600);
        pane.getChildren().add(testedLineChart);
        
        vb.getChildren().addAll(pane, slider);
        
        Scene scene = new Scene(vb, 700, 700);
        stage.setScene(scene);
        stage.show();
    }
    
    private static class ChartsLabelFormatter<Number> extends StringConverter<Number> {
        
        @Override
        public String toString(Number t) {
            return "Form" + t;
        }
        
        @Override
        public Number fromString(String string) {
            throw new UnsupportedOperationException("Not supported yet.");
        }
    }
}

Just move slider to rotate the labels.