lock the form after first signature

In that case, one way of doing it is to open the "Prepare Form" tool => right-click on the first signature field => select "Properties" from the context menu.

The "Digital Signature Properties" dialog window will open up => go to the "Signed" tab => tick the radio button "Mark as read-only:" => if you want the entire document to become read-only select "All fields" from the provided dropdown menu.

Or, if you only want specific fields to become read-only after this field is signed click on the "Pick..." button to select the desired field objects from a list.

Another way of achieving a similar result is by employing a JavaScript script.

You tick the radio button "This script executes when field is signed:" and place a script in the provided JavaScript editing window => click close to exit the Digital Signature Properties dialog window and save your document to commit changes.

See illustration below:

You may also use the guide posted below for additional reference:

• https://helpx.adobe.com/acrobat/using/pdf-form-field-properties.html