In answer to the OP’s question, I’ve never heard of someone being charged a fee just to try a horse, versus a nonrefundable deposit once the horse was out on trial. I have once or twice heard of barns asking if someone trying a horse might want to take a lesson with the on-site trainer. But that would presumably be the standard lesson fee. I also know many people charge someone an additional $10-$25 for lessoning on a barn horse or schoolmaster (on top of the lesson fee), if the student isn’t going to be riding a personal horse or a lease horse.
I have, sadly, known of the practice of many barns tacking on additional fees, in hopes the clients won’t ask what they are. Many clients are ashamed they will look poor/cheap to question a fee, and for fear of seeming ignorant in the face of trainer anger.
But “bookkeeping errors” do seem very common, reading through this thread!
An additional $135 per lesson seems both weirdly specific and incredibly greedy. And even if it was a legitimate fee, it’s certainly significant enough that the client should be told. This is not an emergency situation, and even if the barn doesn’t have a rate sheet (and I hate it when barns don’t), there was ample opportunity to inform the client.