Rebuttal in a journal Recently our paper was rejected in an journal. 

Now, after two resubmissions a Reviewer was not satisfied and the editor sent it to an independent reviewer, who was satisfied with our previous revisions. 

But now he asked a new set of comments and thereby the editor rejected it. 
Our main objection is that the new comments were based on a comment bya  Reviewer and was already answered in the first resubmission. 

So is there any chance for rebuttal as the editor already gave 2 chances for resubmission before? and as the independent reviewer has misunderstood the work and is asking the same question?
Only the editor who rejected the paper can respond to this. But before you send it, be sure that you have somehow addressed all of the objections and improved the paper based on any helpful reviews. 

You don't have to actually do what a reviewer would like, as you still have ownership of the work, but you do need to consider them in any revision. But don't just put in "a few lines" out of context or in rebuttal. Weave any updates into the text. I doubt if you have done this, but including a comment in a paper like "In response to a reviewer we would like to add..." is awkward. That stands out both for the editor and later the reader. 

You can send the editor your best version and ask for reconsideration, but it is up to him/her. If you don't get a positive response, consider submitting elsewhere.