Use a state with objects as options in dropdown menu : REACT

Creating dummy website with a few functional aspects. Just to clarify, I started learning React a week ago so please be kind with your answers. Thank you!

Initially created a state in App.js that allows me to add and delete clients. (like the corny to-do list)

Now using a different component where I can 'add a lesson' I want to have a dropdown selector where I can choose one of the existing clients from the other state as my option. I have created everything so far that takes the inputs and console.log() is showing that everything is going through fine. However, I can't seem to get the dropdown options to show as the existing clients so I can add the lesson in a different state. To clarify I have 2 states, clients and lessons(with the existing clients).

Here is my App.js

import React, { Component } from 'react'
import Clients from './components/Clients'
import AddClient from './components/AddClient'
import NavBar from './components/NavBar'
import AddLesson from './components/AddLesson'

    class App extends Component {
      state = {
        clients : [
          {id : 1 , name : 'bob', price : 30},
          {id : 2 , name : 'mary', price : 40},
          {id : 3 , name : 'greg', price : 45}
        ],
        lessons : [
          {id: null, name: '', time: null}
        ]
      }

      deleteClient = (id) => {
        let clients = this.state.clients.filter(client => {
          return client.id !== id
        })
        this.setState({
          clients: clients
        })
      }

      addClient = (newClient) => {
        newClient.id = Math.random();
        let clients = [...this.state.clients, newClient];
        clients.sort((a, b) => a.name.localeCompare(b.name))
        this.setState({
            clients: clients,
        })
      }

      addLesson = (newLesson) => {
        newLesson.id = Math.random(); 
        let lessons = [...this.state.lessons, newLesson];
        this.setState({
            lessons: lessons,
        })
        console.log(lessons)
      }

      render() {
        return (
          <div className="App">
            <NavBar/>
            <Clients clients={this.state.clients} deleteClient={this.deleteClient}/>
            <AddClient addClient={this.addClient}/>
            <AddLesson addLesson={this.addLesson}/>
          </div>
        );
      }
    }

    export default App;

Here is AddLesson.js

import React, {Component} from 'react'

class AddLesson extends Component {
    state = {
        lessons: [
            {id : null, name: '', time: null}
        ]
    }

    handleChange = (e) => {
        this.setState({
            [e.target.id] : e.target.value
        })
    } 

    handleSubmit = (e) => {
        e.preventDefault();
        this.props.addLesson(this.state);
        e.target.reset();
    }

    render() {
        return (
            <div className="text-center">
                <h2>Add a lesson</h2>
                <form onSubmit={this.handleSubmit}>

                    <select name="lesson_client">
                        <option>{this.props.clients}</option>
                    </select>

                    {/* <label htmlFor="name">Client Name: </label>
                    <input type="text" id="name" onChange={this.handleChange}/><br/>
                    <label htmlFor="time">Lesson Duration (in hours): </label>
                    <input type="text" id="time" onChange={this.handleChange}/><br/>
                    <button className="btn btn-primary">Add Client</button> */}
                </form>
            </div>
        )
    }
}

export default AddLesson

I tried not to overload with code, so if I am missing something, please let me know and I will edit it.