Will quarter windows from an 1984 mustang gt fit in a 1988 mustang LX  

they are both hatchback cars  

Yes, but several modifications are required.

You will have to change the interior quarter trim panels to '79-'86 or trim the '88 panels to fit the '84 glass.  You will have to drill some new holes for the screws, and maybe some for the (front) seatbelt mounts.

The '88 drip rail molding will have to be changed to '79-'86.  If you have a T-roof (not very likely in '88) you will need T-roof drip rails.  If you have a solid roof you will need solid roof drip rails.

The '88 trim on top edge of the doors will not match the '84 quarter glass trim.  If you want to remove the trim you will have to fill the holes in the door skin, and also might want to change the mirrors to '79-'86 style since the '88 mirros will have a tab sticking out with nothing to match to.  You would need '79-'86 trim for the doors and the matching "dew wipes".  '70-'86 mirrors are not power.