Some patients claim that laser hair removal also lightens the skin complexion like the underarm for example. How true is it?

i dont think it lightens the skin itself, but makes it appear so because the roots are removed, compared to the darkness of the roots after shaving it makes a big difference.
also, waxing the underarms causes darkness in many people so after doing laser they are relieved from that too.

Laser Hair Removal removes follicles and stubble to a high extent, which gives the illusion of a lighter skin tone. However, in reality, this is only an ilusion as laser hair removal solely gets rid of hair and hair only.

Laser hair removal in the armpits not only erase hair growth, it also removes the hair follicles in the area resulting in lightening of the skin 

At first you will see it's lighten the skin.But after a week the skin appear darker.I recommend hair removal cream.It's safe and not harming the skin.

it can happen but more prone to darker skin types. its very important for the client to maintain their skin at home after having laser.  By incorporating appropriate homecare

laser hair removal of the armpits works on absorbing the pigment so if there is any hyperpigmentation it might become lighter

No.This is not right.Laser removal does not lighten the skin.This is a wrong opinion.

skin after hair removal does not become lighter

yes it will lighten the skin as the laser treatment , penerates the skin layers and reduce the melanium of the skin 

yes it will lighten the skin 

40 %... as the hair removed.. widepores lessen and black appearance that it may results abate.

Yes,It does lighten the axila area where the follicle of the  hair is strong