Welcome.
Just buy a new cable, you need a new one anyways. As for the carbs, Id probably spray any sort of lubricant in there just to wet it up a bit. You still wont be able to touch the butterflies in the carbs because youll have the slide blocking it. You should be able to use a small screwdriver and gently lift the slide to get some lube in there. The slides arent connected to anything except fragile rubber diaphragms that you wont have access to until you remove the tops of the carbs. More than likely its a seized throttle cable..
If you plan on riding the bike down the street, you have a small list of things to check off.
You need to completely rebuild the brake system, including new brake lines. You will need a new battery. Youll need new tires. Youll need to change the oil and probably replace a couple seals along the way. You need to go over all the maintenance with the engine.
At the very least, you need to replace the cable and go over all the engine maintenance and get a new battery, and give the carbs a really good cleaning, add an inline fuel filter too. This should be just enough to get it started assuming the bike was running when it was parked. Make sure to take the head caps off and squirt oil all over the lifters and cams and even in the spark plug holes, its probably all bone dry