Getting changeType Attribute in Edit Trigger Google Apps Script

From the question

Could a script be run when the user sets the delete column to Y

Yes, it's possible by using an on edit simple/installable or on change installable triggers.

References

• https://developers.google.com/apps-script/guides/triggers

You need onFormSubmit, not onEdit. Open the documentation of classes Spreadsheet, Sheet, and Range, and look up each of the methods used below. To give you a general idea of what is done here:

1. ss = active spreadsheet, sheet = active sheet
2. values = an array of values in the active sheet. Note that arrays in JavaScript are 0-indexed.
3. row = the row added to sheet when the onFormSubmit event happened. This one is 1-based, so the adjustment row-1 is used when addressing arrays.
4. values[row-1][1] - the value in column B of this row. [Row number][Column Number] in 0-based indexing.

The script isn't perfect. For one thing, it assumes the target has rows available. You may want to use insertRowAfter() to be safe. Or just create a lot of rows. The logic for other things you mentioned is not here either, but it's essentially the same.

function onFormSubmit(event) {
  var ss = SpreadsheetApp.getActiveSpreadsheet();
  var sheet = SpreadsheetApp.getActiveSheet();
  var values = sheet.getDataRange().getValues();
  var row = event.range.getRow();
  if (values[row-1][1] == 'Luke') {   // column B in 0-based indexing 
    var targetSheet = ss.getSheetByName('for Luke');
    var lastRow = targetSheet.getLastRow();
    var targetRange = targetSheet.getRange(lastRow+1, 1, 1, values[0].length);
    targetRange.setValues([values[row-1]]);
  }   
}