The LS tranny has longer gears, ment for the economy car it was built for.
The GSR tranny has shorter gears, ment for the sportier car it was built for.
I dont know if the dude above me thinks you have to take apart your automatic trans to 'convert' it to manual or what but that's not at all the case. You seem to already know that you just have to swap the entire tranny so i'll just let that be.
Some of the parts you'll need are, the shift linkage and shifter assembly, transmission of course, pressure plate, clutch disc, flywheel, possibily a different transmission mount and possibly a new rear motor mount, high temp wheel bearing grease, possibly axels.
i've never converted an integra to manual, but thats an overview for most swaps.