The only way to really know for sure is to see the flowers. K. luciae flowers white while the other species flowers yellow (sometimes gray-green). The leaves are not necessarily all that different, vegetatively the plants tend to be extremely similar. K. luciae will branch more often and earlier, especially the forms in cultivation.
Until very recently luciae was vastly more common in cultivation than the other species, which was essentially only found in botanical gardens or hard core specialist collections. But I saw thyrsiflora was recently (last year or two) being produced in numbers, and this simple distinction is likely to be less and less useful over time.
Regardless, when in doubt, guess luciae. Based on sheer numbers, you will most likely be right.
More info about those species here:
https://www.smgrowers.com/info...