My 19 year old step son lives at home, his father doesn't charge him rent or expect him to do much around the house. He doesn't go to college although all of his friends do and he could if he applied but he hasn't taken the initiative, he works part-time for his father, less than 20 hours a week. His father is very generous with his pay and also gives him off almost every time he asks to go places/trips with his friends. He likes to stay up at night playing computer war games and sleeps all day. He usually gets up around 4:00 p.m. and stays in his room playing games or is on his phone. He compares his life to his rich friends who go to college and parent's pay for everything and says he is depressed. The doctor put him on 50 mg of Zoloft six months ago but it doesn't seem to be helping. He tells us to stay out of his business and doesn't want to discuss anything with us. Recently we told him he had to get up by noon so he is awake but still lays in bed texting/reading on his phone. Not sure what else to do. He has a good life and thinks his life should be better when he compares his life to his rich friends.
and says he is depressed.
This sounds like you don't believe your step son.
The doctor put him on 50 mg of Zoloft six months ago
On the other hand sounds like the doctor also thinks he is depressed, as according to the internet:
Zoloft is the brand name of sertraline, an antidepressant used to treat major depressive disorders.
Major depression isn't just laziness or something that can be easily changed just by willpower without help. One the hardest part of being depressed is that family members and friends do often not know what it means being depressed, and despite having the best in mind and just being encouraging someone depressed to just do something with their lives can make it worse. Yes, there is a chance that he might be making this up, or he is exaggerating. At the same time, there is very little risk in trying to learn more about this.
My suggestion would be to read about depression and take the possibility that your step son might suffer under depression seriously. I recommend the book "Shoot the damn dog" by Sally Brampton, which I believe describes very well how it feels to live with depression.
Personal Opinion based on previous experience as that 19 y/o:
His father and you are enabling his entitlement. He feels that he deserves the same things his rich friends have, and he isn't developing any usable skills to further himself. If he is getting paid to do minimal work than he is going to expect that when he is forced out of the house and actually has to work. I feel you are doing him a great disservice by allowing him to continue this way.
What happens when he's 21? 25? 30? I don't imagine you're going to want him still living in your house. Where will he be able to get a job that has such minimal hours with such high pay? I feel that you're enabling is creating a consequence-free atmosphere that is highly unrealistic and unattainable outside of him living in your home.
I suggest a serious conversation with your husband about the boy's future. What does it look like? Should he enroll in a few community college courses? Should you implement daily chores? Should he start working more hours? Should he start paying rent/car insurance/etc? Find ways to start increasing his independence. You want this baby bird to be able to fly when the time comes, not fall flat on his face to the point where you have to bail him out and resuce him, again, because he's not ready for the real world.