While lumens are primarily designed to be used for human vision, they are typically all we have to go with. Human vision is most sensitive to green light and photosynthesis is least sensitive to green light so you see the problem. Common lights are rarely rated for PAR (photosynthetically active radiation) Watts. Lumens measure the amount of visible light put out by a light source so there are other issues with using them.
lumens (the unit) is not all that helpful for plants bigger than cuttings. With most cuttings the total leaf bearing length of the stem is usually less than 6 - 12". With the lights 4 - 6" from the leaves the lumens per square foot of illuminated surface isn't all that different from one person's setup to another's.
When you have a 3' plant and 1 light source, the light may be 6" from some leaves but 2.5' from others. You're all familiar with the inverse square law - the amount of light falling on an object decreases with the square of the distance. So if the bottom leaves are 5x further away they're getting 1/25th (4%) of the light that the upper leaves are getting. There's no way a plant can stay healthy if that light source is a 6,000 Lm fixture.
The units you need to measure are based on how much light the leaf surfaces actually receive. That means how much light per unit of leaf surface area on the leaf, not at the light source. That's measured as Lux (Lumens/sq meter) or Foot-Candles (Lm/sq foot). Optimum photosynthesis occurs at 2000 FC (21528 Lux). You might be able to keep a fig plant alive at 600 FC (6458 Lux) but the growth will be weak and lanky and is likely to break, especially if in later years it has to support fruit. The minimum I'd attempt to grow a fig at is 1000 FC or 11,000 Lux. And that's on all leaves. You'll need several lights surrounding the tree to make that happen.
The other issue is will Brown Turkey ever produce fruit that tastes good that way. In general people who grow BT in Z6 say it doesn't get the heat or season length it needs to ripen well so it doesn't taste good here. Will lights change that? You'd have to find out. 1,000 FC might, 2000 FC (for 8 -16 hrs per day) probably would as that's the maximum amount of light a plant can use. You'd also have to keep it between around 82 - 90 degrees F (just an educated guess) to get the fruit to ripen properly. I think you'd be better off with a Hardy Chicago or Salem Dark which can ripen good figs in less optimal conditions.
