An atheist way of life is one that doesn't follow the rituals and live by the religious year.
Although I'm not an Atheist, I would say much of my life is an "atheist way of life."
My Christian friends life is punctuated with seasons and the bible is followed seasonally and she regularly attends church.
An atheist could follow it and give up things for lent, but is there any point? Other than giving to charity and joining in a religious community.
An atheist lifestyle doesn't put religion or I should say God in its priorities, whereas a religious one does.
A Muslim prays so many times a day, no atheist is going to bother
Well if they did, I'd wonder why