Converting between Nike and Lululemon trips people up because the two brands are cut differently. Nike is fairly true to size, while Lululemon is fairly true to size. Nike and Lululemon fit fairly similarly, though cut and fabric still shift things style to style. The converter above corrects for this automatically by reading the body-measurement range behind each size rather than matching the letter on the tag.
As a quick guide: a size S in Nike converts to about a S in Lululemon, a M lands around a M, and a L is roughly a L. When your measurement falls near a boundary the tool flags it as a between-sizes case — worth checking the garment's own measurements before you order.