Can i use 225 55 16 on my gs 300 2002 sport design

Sure you can.

The Lexus website shows 215/60-16 tires as standard on the 02 GS300: http://www.lexus.com/contact/pdf/2002/2002GSspecs.pdf
It also shows 225/55-16 all season tires as optional on the 02 GS430.

There is no reason good you can't used the same 225/55-16 tire size that came on the GS430 on your GS300.

If your speedometer is accurate with 215/60-16 tires, it will read 1.584% too fast with 225/55-16 tires.
If your speedometer is accurate with 215/60-16 tires, it will read 0.075% too fast (virtually dead-on accurate) with 235/55-16 tires.

If keeping your speedometer reading the same is important, when staying with the same wheel size (16") and going to a "+0" setup, one increases the section width by two sizes (to 235) and reduces the profile by one size (to 55).

You can view the effects of different tire sizes at http://www.1010tires.com/TireSizeCalculator.asp

If your car has the navigation system, you can probably see your true speed our your car by looking at the speedometer on it. The handheld GPS I used for hiking is surprisingly accurate for showing vehicle speed -- at least the speed it shows matches the aftermarket Magellan GPS I use in my car which is about 2-3 mph slower than what my car's speedometer says at 70 mph with new OEM size tires.

thanks alot

you can... i concur...