Oh it's definitely a lie.

Smith named Stewart — and included a website service request from him, listing his phone number and email address in 2017 court documents. But Stewart told The Associated Press he never submitted the request and didn't know his name was invoked in the lawsuit until he was contacted this week by a reporter from The New Republic, which first reported his denial.

"I was incredibly surprised given the fact that I've been happily married to a woman for the last 15 years," said Stewart, who declined to give his last name for fear of harassment and threats. His contact information, but not his last name, were listed in court documents.

He added that he was a designer and "could design my own website if I need to" — and was concerned no one had checked into the validity of the request cited by Smith until recently.

https://www.npr.org/2023/07/01/1185632827/web-designer-supreme-court-gay-couples

And this came out before they released their decision. So they knew it was a lie.