Develop a Python script that connects to an AWS Lambda function, sends a JSON payload containing two numbers, and receives the sum of those numbers as a response from the Lambda function.

To achieve this, you need to create an AWS Lambda function that accepts a JSON payload containing two numbers and returns their sum. Then, use the `boto3` library in Python to invoke the Lambda function.

First, create the Lambda function:

1. Sign in to your AWS Management Console.
2. Navigate to the Lambda service.
3. Click on "Create function".
4. Choose "Author from scratch", give your function a name (e.g., "addNumbers"), and choose a runtime (e.g., "Python 3.8").
5. Create or select an existing execution role with basic Lambda permissions.
6. Click on "Create function".

Now, replace the default code in the "Function code" section with the following code:

```python
import json

def lambda_handler(event, context):
    num1 = event['num1']
    num2 = event['num2']
    
    result = num1 + num2
    
    return {
        'statusCode': 200,
        'body': json.dumps({'result': result})
    }
```

Save the changes by clicking on "Deploy".

Next, install the `boto3` library if you haven't already:

```bash
pip install boto3
```

Finally, create a Python script to connect to the Lambda function and send a JSON payload:

```python
import boto3
import json

# Initialize a Lambda client using your AWS credentials
client = boto3.client('lambda', region_name='your_region', aws_access_key_id='your_access_key', aws_secret_access_key='your_secret_key')

# Define the input data as a dictionary
input_data = {
    'num1': 5,
    'num2': 7
}

# Convert the input data to a JSON string
payload = json.dumps(input_data)

# Invoke the Lambda function and pass the JSON payload
response = client.invoke(
    FunctionName='addNumbers',
    InvocationType='RequestResponse',
    Payload=payload
)

# Read the response from the Lambda function
response_payload = json.loads(response['Payload'].read())

# Extract the sum from the response payload
sum_result = json.loads(response_payload['body'])['result']

print(f"The sum of {input_data['num1']} and {input_data['num2']} is: {sum_result}")
```

Replace `'your_region'`, `'your_access_key'`, and `'your_secret_key'` with your AWS region, access key, and secret key, respectively.

Run the Python script, and it will connect to the Lambda function, send the JSON payload containing two numbers, and receive the sum as a response.