Gst to sez: should i take lut for my company?

We are supplying auto machine parts, and also involve in supply designs and fabrications.

Some of our customer are asking invoice without GST based on a SEZ letter they have obtained. 

Is it OK to provide them invoice without GST? Will I be in any trouble? 

Also should I pay the GST for such invoice to the government?

If I sent invoice without GST to customer but pay GST, then I am paying tax for them? They are telling I have to take LUT.

Or should I not pay GST for such invoices since they are also not paying? 

Please advice on this issue

Thanks & Regards.