Within India supplies or sales no need of LUT or Bond. Please go through the followings:
(a) You have to sales showing either (i) IGST or (ii) SGST+CGST in Tax Invoice. Exceptions to exempted items (no needs to show tax parts).
(b) One more point if you are Composite Dealer than you have to raise Bill of Supply not Tax Invoice (you couldnot collect tax from the Buyer, hence you couldnot show tax parts in your Bills)
(c) "If you are supplier and supplying your deals in to a exporter"- The concept is wrong. You couldnot treat the Buyer as Exporter. Under GST, you should categoried this type of Buyer in B2B (i.e. Business to Business)
I am not an expert to comment. But what I know I have shared from the very question you have asked and I understand.
Thanking you
Santanu K Baruah