Invalid left hand side assignment onclick javascript button

You have a few problems with your code. Let's start with the first one: Boolean values are not capitalized in JavaScript, and JavaScript is case sensitive. That means you should use true and false instead of True and False.

Secondly, there's no reason you need to compare to true or false directly; simply use the value for true, or its inverted value for false. Third, you can combine all of your checks into a simple formula:

if({!Lead.Content_Approval__c && NOT Lead.Relations_Approval__c &&
 NOT Lead.Final_Approval__c && Lead.Approval_Confirmation__c &&
 NOT Lead.Relations_Approval_Confirmation__c && NOT Lead.Approved__c}) {
  if(confirm(...)) {
    // Do action
  } else {
    // Go back
  }
} else {
  alert(...);
}

Finally, you can write a slightly more optimized version by swapping around some Boolean logic:

if(
{!
AND(
  Lead.Content_Approval__c, Lead.Approval_Confirmation__c,
  NOT(OR(
      Lead.Relations_Approval__c, Lead.Final_Approval__c, Lead.Relations_Approval_Confirmation__c
    )))}) {
  if(confirm(...)) {
    // Do action
  } else {
    // Go back
  }
} else {
  alert(...);
}

You can do this because NOT x AND NOT y is the same as NOT(x OR y).