When I initially read this I thought it was so strange that therapists and other (regular) people don't understand what limerence is because limerence is all over romance movies. It's more common to see limerence than true love in popular romances! Then, I realized people don't recognize it because they are misinterpreting the limerence they feel as "love" because they've been taught (via society) that it is love, or at least puppy love or unrequited love.
A famous example of limerence is how Andrew Lincoln's character feels about Keira Knightley's character in "Love Actually". That movie is full of limerence, but that part of the movie is the most obvious example.
Yes, I think the friends / therapist understood it to be unrequited love.
This is more of an obsession though. It can completely take over the person's thinking. They can lose focus on everything else. There can be extreme emotional highs if the limerent object appears to reciprocate and extreme lows when it's clear they are not interested. This can last for years.
The therapist had not heard of the term limerence. She didn't seem to think it was a problem. She wanted to focus on the anxiety and perhaps this was the right approach.