Begin by exporting your data from Zendesk Chat. Log in to your Zendesk Chat account, navigate to the 'Settings' tab, and select 'Account'. From there, choose 'Data Export'. You'll typically have options to export chats, agents, and other relevant data. Choose the appropriate format for export, such as CSV or JSON, which will be compatible for later processing. Follow the prompts to download the exported file to your local machine.

Before moving data to Databricks, set up your local environment to ensure you have the necessary tools for data processing. Install Python and relevant libraries such as pandas for data manipulation, if not already installed. This will help in cleaning and transforming the data if necessary. Ensure you have sufficient storage and a working directory to manage the files.

Open the exported file using Python pandas or any other data manipulation tool you prefer. Perform necessary data cleaning and transformation tasks. This could include removing duplicates, handling missing values, converting data types, or restructuring the data to fit your desired schema. Save the cleaned and transformed data back to a CSV or JSON format, depending on your preference and needs.

Log in to your Databricks account and navigate to your Lakehouse workspace. In the workspace, create a new cluster or use an existing one that is configured to handle your data processing needs. Ensure that the cluster is running and that you have appropriate permissions to import data into the Lakehouse.

Use the Databricks web interface to upload your cleaned data file to the Databricks File System (DBFS). Go to the 'Data' tab in your Databricks workspace, click on 'Add Data', and then 'Upload File'. Follow the instructions to select your local file and upload it to your desired directory in DBFS. This will make the file accessible to your Databricks notebooks.

In a new Databricks notebook, use PySpark to read the data from DBFS into a DataFrame. Use the following PySpark code as a template:
```python
df = spark.read.format("csv").option("header", "true").load("/dbfs/your-directory/your-file.csv")
```
Adjust the format and options if your file is in JSON or another format. Once the data is loaded into a DataFrame, create a table in the Lakehouse:
```python
df.write.format("delta").mode("overwrite").saveAsTable("zendesk_chat_data")
```

After loading the data into a Databricks table, verify its integrity by running basic queries to ensure that the import was successful. Use SQL commands within a Databricks notebook to validate the data:
```sql
SELECT * FROM zendesk_chat_data LIMIT 10
```
Check the number of rows, data types, and sample data to ensure everything is in order. Make necessary adjustments if any discrepancies are found.

By following these steps, you can efficiently move data from Zendesk Chat to Databricks Lakehouse without relying on third-party connectors or integrations.