It is greatly affected by where you live, and the time of year, among many other factors. Right now, in my part of the country, the riding season is coming to an end by the end of this month or mid-November. Like the tide raising and lowering all boats, this deflates the price of all used bikes around here. A bike that would have fairly quickly sold for $3300 in April or May, will now generally bring in the lower $2200-2500 range this month. Where you can ride year round, the price may be more stable.
Certain models, like R65LS, are also very popular in certain areas, like around San Fransisco, which drives up the price.
I think that if the bike is in great mechanical shape, and good-to-very good cosmetic condition, you can get in the low to mid $3K for a documented R65. If it needs mechanical stuff beyond shocks or tires, you'll be in the mid $2K range or lower.
If your LS is in excellent condition with perfect paint and mechanicals and is painted in an original color, you could get in the $4K - $5K range for it if you time the sale right. But around my neck of the woods, NOW is the time to go bike shopping if you are a buyer because there ARE $3K bikes going for $2K prices because of the impending white season.
When I bought my 82 R65LS about 6 or 7 years ago, I paid $2400 for it. It had all its parts, original paint, and was ridable, but needed work. I've got around $1700 additional into it now - it is mechanically great but needs to be repainted to be close to perfect for me, but still not concours. It is a labor of love though, I don't think that I'd want to sell it, even if I could miraculously get back what I have into it, which is unlikely. So, with paint (body and wheels) it will have cost me close to $5K over the years, but I will certainly have more than $5K worth of enjoyment out of it in the end.