Lumens measure visible light, and are weighted based on the sensitivity to the human eye (which peaks in the greens.)
Photosynthesis occurs from light in the deep red and deep blue ranges, of which the human eye sees very little. Greens don't help much, if at all.
Everyone has different bulbs, outputting different spectrums at different efficiencies with different quality reflectors. I truly don't believe you can quantify it in watts per gallon or lumens per gallon or anything else per gallon.
Maybe if manufacturers started rating their bulbs based on a unit of brightness which is weighted for photosynthetic activity, there would be a proper way to select a lightbulb.