I have found that the HKS-36 speed loaders work with the KLCR fine, meaning for me with a little "maneuvering". The BEST I found were the 5-STAR speedloaders, work just perfectly. They cost a little more, but work much better than the HKS for ME. Just a suggestion.
I own them all, HKS, SL Variant, and 5 Star, for my LCR, (and Safariland for my Security 6 and GP.) The only one that actually fits the "cylinder bullet circle" on the LCR is the 5 Star. (The one specifically for the LCR, the J2 36) With the 5 Star you can seat the speed loader fully into the cylinder and spin it, at least with Crimson Trace grips. The 5 Star could be better (in my opinion) if the shells did not rattle around in the holder, as it makes it a little harder to line them up in the cylinder without a little more jiggling than the other speed loaders require. However, once the shells are seated in the cylinder, the 5 Star releases them cleanly and efficiently. All things considered, I concur with Rxdoc, the best speed loader for the LCR is the 5 Star.
I use both the HKS-36 and 5 Star with my SP-101 and LCR-357. The SP has CT laser grips and the LCR is stock. The 5 Star seem to work a little better and i like the solid aluminum construction, both seem to work better with the shorter .38 spl. rounds. The 30 round loading block is great for use at the range too. Two weeks age i got a pair of 5 Star loaders and 10 round block for my SP101-22 and it works great too, would have liked a 30 or 40 round block but only the 10 round was available.