A fire door in our office has a 6mm gap on the hinge side & 3- 3.5mm on the closing side. What is the best way to reduce the gap on hinge side to get 3-4mm.

There is no quick and easy way to do this.  Remove the door and loosen the door frame fixings so that the door frame hanging jamb can be moved-over and then re-install.  You will need to check the gap between the surrounding wall and the doorframe is correct and make good the fire-stopping between the wall and door frame.

Depending on the gap issue, you may have to completely remove the door assembly and re-install.

Can the door be lipped?

Lipping depends on what fire performance certification exists for the door.   I like lipping done correctly, but carrying out such work on site may void the door's third party certification.