7 watts? That won't do 400 lm for long.

On the first, no way are you going to draw 7W out of an AA and I'm not sure it's safe in a Li-ion 14500 cell - that's a 2.5C draw. You really don't want to stress Li-ion cells.

On the second, 3 AAA's are not going to produce 7W but a Li-ion 18650 can do it safely. However 7W way too much heat on the LED without more aggressive heat-sinks than I see.

I'd expect that in the real world they'd deliver less than 150-200 lm. Good price regardless.