版本如下：

"dependencies": {
    "axios": "^0.18.0",
    "react": "^16.8.6",
    "react-dom": "^16.8.6",
    "react-router-dom": "^5.0.0",
    ...
  },

App.js代码片段:

...
<Route path="/lesson/:id" exact render={props=>
            <Lesson 
              base_url={URL} 
              isLogin={this.state.isLogin} 
              token={this.state.token} 
              username={this.state.username} 
            />
          }/>
...

Lesson.js代码片段：

...
componentDidMount() {
        let id = this.props.match.params.id;
        axios({
            url: '/app1/lesson/' + id + '/',
            headers: {}
        })
        .then(更新状态)
        ...
    }
...
render(){
    return 
        ...
        <Row>
                          <Col>
                            {lesson.prev_id>0?
                              <Button 
                                variant="outline-info" 
                                onClick={()=>this.props.history.push('/lesson/'+lesson.prev_id)}
                              >
                                  上一课：{lesson.prev_title}
                            </Button>
                            :<div/>}
                          </Col>
                          <Col 
                            className="col-center"
                          >
                            <Button 
                                variant="outline-info" 
                                onClick={()=>this.props.history.push('/course/'+lesson.course_id)}
                            >返回课程列表</Button></Col>
                          <Col className="col-right">
                              <Button 
                                variant="outline-info" 
                                onClick={()=>this.props.history.push('/lesson/'+lesson.next_id)}>
                                    下一课：{lesson.next_title}
                              </Button>
                           </Col>
                      </Row>
        ...
}

现在的问题是，Lesson页面加载后，单击“上一课”、“下一课”，浏览器地址栏改变，页面不重载，显示仍然是初次载入后的数据。

经查这个页面：

...
Along with componentDidMount, You also need to implement the componentWillReceiveProps or use getDerivedStateFromProps(from v16.3.0 onwards) in Products page since the same component is re-rendered with updated params and not re-mounted when you change the route params, this is because params are passed as props to the component and on props change, React components re-render and not re-mounted.
...

意思是页面加载后，参数是作为属性props传入的，属性的改变并不会导致页面部件更新，状态state的改变才会。

于是将axios获取数据放入单独函数fetchLesson中，增加componentWillReceiveProps函数：

componentWillReceiveProps(newProps) {
        let id = newProps.match.params.id;
        if (typeof(id) !== 'undefined' && id !== null && id !== this.props.match.params.id) {
            console.log('will fetch new lesson...')
            this.fetchLesson(id);
        }
    }

componentDidMount修改如下：

componentDidMount() {
        let id = this.props.match.params.id;
        this.fetchLesson(id);
    }

问题解决。