No conversion between the 2. Like you said Kelvin or K-rateing is color temperature. Lumens is a measurement of output based on what is seen by the human eye. Lumens isn't used,in the case of aquarium plants, as apposed to the watt per gallon method because the human eye is more responsive to the yellow and green colors of the spectrum. The yellow/green have little effect on plant growth. The blue/violet are more imporatnt along with the red/orange. I think the ratio is 2 units blue/violet to 1 red/orange. Usually bulbs that are above 5500K are marked with a K rateing. I am speculating because of the rare allergy to natural sunlight some suffer from. 5500K is approx. = to the suns spectrum at 12 noon. For the most part anything labeled cool white, soft white are below 5000K. Ones with full spectrum, or sunshine are usually