Probably not what youre looking for, but similar to the way there are doctors offices that only write perscriptions for medical marijuana, there are counselors that specialize in writing scrips for emotional support animals. Maybe if you cant get one through lyra, you can use one of those services.

Finding ESA certificates online is very easy, or it used to be. Laws have since cracked down on it a lot recently.
Although connecting with a mental health professional and doing to the "right way" is way more useful in the long term.
Background: I was moving out of the country and NEEDED my dog. I tried without him for a month and it was bad.I asked my PCP/main Dr. But I needed an appointment, to get a referral. Then get on a huge waiting list. Saying all this just so people don't go all Karen.

And yeah, ESA and service animals are very different. But service dogs for anxiety are a thing. I don't know much besides that though