Does Lumosity make any claims about improving autism conditions? It's a pretty big leap of logic to believe that a generic brain game system should improve autism range conditions.
http://autismsd.com/lumosity-and-autism/
http://tarf.nereanieto.com/tag/lumosity/
"Treats autism" is a medical claim so Luminosity would need to be very careful if they did ever make that claim. Which makes me gently suspicious of all the blog coverage. And specialist blogs for medical conditions can be full of cranks.
That was my first objection to my family members.
Lumosity does however make claims on brain improvements.
Calling Lumosity bullshit due to some expectation towards it that it doesn't make is akin to calling vitamin tablets bullshit because they don't cure diabetes.