My trottle handle only move slowly when returning to idle. Is there a special way to lubricate the wire?

The OEM cable is Teflon lined and should not need any lube but if it has been done with some oil it is likely to have gathered dust and dirt so may need cleaning. If you have heated grips that are genuine BMW then remove the right grip and make sure the cable to the heated grip has not bunched up at the end of the handlebar. I have had to fix the bunched up cable twice in about 10 years on my wife's K75.
Also it is quite possible the handlebar under the grip and the gear mechanism under the plate next to the master cylinder need some moly lubrication as it does dry out and cause the grip to get sticky.

The grip might also have been pushed onto the throttle tube far enough for its flange to make contact with the cable housing creating friction that slows its return. Pulling the grip away from the housing slightly will remedy that.

Not only was my throttle return sluggish, but I was blowing Fuse #1 when I used the heated grips.  Turns out the master cylinder/throttle on my K75RT had been pushed onto the bars so the heated grip wire was pulled against the end of the bars wearing away the insulation.  After I repaired the worn insulation I slid the assembly out about 3mm. 

Problem solved.  No more electrical problems and a snappy throttle return.

There is a screw that applies friction to the throttle grip that reduces effort to maintain a throttle position. Not quite a cruise control, but I find them useful.
https://www2.munichmotorcycles.com.au/product_info.php?cPath=2804_1698_2204&products_id=565

If one of those is on your bike, you will see it under the handlebar throttle housing. Remove it and see if there is a difference.

Many bikes didn't have this, so it may not be your problem, but it would be annoying to do lots of other harder things if that is the problem.

Bill

All the 2V Ks have slow throttle return.

What I do is clean out the old grease in the cog of the throttle parch and then lubricate them with silicone spray.

Take out the big Phillips screw next to the front master reservoir to take off the plate above the cog to access the cog.

RicK G wrote:The OEM cable is Teflon lined and should not need any lube but if it has been done with some oil it is likely to have gathered dust and dirt so may need cleaning. If you have heated grips that are genuine BMW then remove the right grip and make sure the cable to the heated grip has not bunched up at the end of the handlebar. I have had to fix the bunched up cable twice in about 10 years on my wife's K75.
Also it is quite possible the handlebar under the grip and the gear mechanism under the plate next to the master cylinder need some moly lubrication as it does dry out and cause the grip to get sticky.

I have not lubricated the wire, and I do not know if any of the former owners have done so. I just asked because I thought it might be an option. Now, of course, I will not persue that line. I also checked the mentiones screww and the position of the handle bar. There is no screw by the main reservoir, and the handle is at least 5 mm away from the switch/starter/stop cluster.

Do not use WD 40 if you are going to lubricate any cables, apparently WD 40 can break down the Teflon liner. You can use a PTFE based lubricant called Triflow which can be obtained from bicycle shops.
Regards Martin.