At 8 MJ (2000 kcal) / day = 90W (average) diet, to scrub CO₂ you would need to bind about that much energy on average¹. Assuming optimistic 50% LED efficiency a

At 8 MJ (2000 kcal) / day = 90W (average) diet, to scrub CO₂ you would need to bind about that much energy on average¹. Assuming optimistic 50% LED efficiency and 90% algae efficiency², you would need at least about 90W/50W / 0.5 / 0.9 = 4x as much production. So your setup could not scrub a typical person's CO₂. Nevertheless, fully optimized 17l of algae do seem believable, if well cared for. ¹ ignoring diet levels and differing CO₂ / H₂O ratio for fat vs. carbs etc. ² no idea how efficient algae are, but wikipedia says they are very efficient