I’m doing the throttle tube mod with the r6 throttle. I saw online it’s recommended to use grease before putting on the new tube I have some copper grease here would that be any good or should I buy something better.
I've found that it's best left clean and dry. Grease will attract dirt, gumming up the works. If you insist on using a lubricant, use a dry-film lubricant of some sort - Teflon, silicone, or some such thing.
Yeah I did it without lube and sometimes it sticks slightly at the very end of its throw. Leaves me about 200RPM above idle. I plan on disassembling and applying some lithium grease when it gets warmer out.
If the amount of sticking depends on which way the handlebars are pointed, check cable routing and check if the cables are over-tightened. Tangled/pinched/bent-too-tightly throttle cables will lead to excessive friction in the cable - but it will tend to vary depending on which way the handlebars are aimed.
The other thing to check for, is whether the soft grip part of the throttle tube is rubbing against the switch housing or the bar-end. It shouldn't. If it is, it will want to stick.
In addition to what GoFaster said above; get the (enhanced) manual here, then refer to page 137, section 3-26 for "Check the Throttle Grip Operation".
In the Enhanced Service Manual, I included links to make navigation pain-free.
Regardless of the year your bike is, your Throttle Grip will have the same mechanics and operation.