I've done lots of reading up on it, and lumens are very very useless for plants, the right unit for plant growth is PAR. The reason is plants use blue and red light to grow, they don't use [much] green light which gets reflected making them look green. And we essentially evolved to see what the plants don't use (green). Lumens is defined as brightness as it appears to the human eye, where PAR is defined as useful brightness as seen by plants, and if you're following my description, they end up being almost opposite units.
I explain it in more detail on my website
and I got a calculator that is capable of converting between lumens and PAR linked there, but the result is you can't convert between the two without knowing the spectrum of the light, for incandescents and halogens the color temperature is a good measure of the spectrum, but for other lights (LED and florescent) it is NOT a good measure of spectrum. Also of importance, most cheap light meters assume a spectrum when measuring (they have a non-linear response curve with respect to the spectrum), for lights with very odd spectrums (like purple grow lights), this may make cheap meters useless as well.