Begin by setting up an account on Databricks if you haven't already, and create a new workspace. In your workspace, create a new cluster. Choose the appropriate configurations for your cluster, such as the instance type and the Databricks runtime version. Ensure your cluster is running before proceeding with the data transfer process.

SpaceX offers a public API that allows you to access various datasets. You can find documentation and endpoints for the SpaceX API at [SpaceX API Documentation](https://github.com/r-spacex/SpaceX-API). Use Python's `requests` library within a Databricks notebook to send HTTP requests to the SpaceX API and retrieve data. Begin with a simple GET request to fetch data, for example:
```python
import requests

response = requests.get('https://api.spacexdata.com/v4/launches/latest')
data = response.json()
```

Once you have retrieved the data from the SpaceX API, parse the JSON response to extract relevant fields. This involves understanding the structure of the JSON data and selecting the fields you are interested in. You can use Python's built-in JSON handling capabilities to navigate through the data structure.
```python
launch_data = {
'name': data['name'],
'date': data['date_utc'],
'rocket': data['rocket'],
'success': data['success']
}
```

Convert the parsed data into a format that can be easily uploaded to Databricks. A common approach is to use pandas to structure the data into a DataFrame. This helps in managing the data effectively and provides a seamless way to write it to a Databricks table.
```python
import pandas as pd

df = pd.DataFrame([launch_data])
```

Databricks FileStore allows you to store files that can be accessed within your Databricks environment. Save your DataFrame as a CSV file and upload it to the FileStore. This can be done using the `dbutils` library in Databricks.
```python
df.to_csv('/dbfs/FileStore/tables/spacex_launches.csv', index=False)
```

Use SQL or Python to create a table in your Databricks Lakehouse to store the SpaceX data. You can execute SQL commands within a Databricks notebook to define the schema of the table and ensure it matches the structure of your data.
```sql
CREATE TABLE IF NOT EXISTS spacex_launches (
name STRING,
date STRING,
rocket STRING,
success BOOLEAN
)
```

Finally, load the data from the CSV file in the FileStore into the table you created in the Databricks Lakehouse. You can use SQL commands within Databricks to achieve this. The following command reads the CSV and inserts the data into the table:
```sql
COPY INTO spacex_launches
FROM 'dbfs:/FileStore/tables/spacex_launches.csv'
FILEFORMAT = CSV
```
This sequence of steps guides you through retrieving data from the SpaceX API and transferring it to a Databricks Lakehouse, without relying on third-party connectors or integrations.