You know that unless you're very experienced with siderreins, your horse isn't actually collected and/or working off of her topline, right? I've yet to actually see anyone correctly use sidereins in front of me. (Youtube has a few people...). Sidereins usually make the horse tense and behind the bit/movement, even in horses used to wearing them.
TBs generally aren't lunged on the track. This is probably pretty new to her. Most OTTBs come off the track and develop arthritis at an early age. Your mare might be developing arthritis in the hocks, if they're ouchy from lungeing.
I personally dislike lungeing anyway, as it puts a lot off pressure on the joints and puts the horse off balance. Free lungeing is the way to go. :)
Throw her on some MSM (10,000mg per dose, takes a week to start working). If it helps, you know she's got some joint issues. Take her off it in a month or so and if she's ouchy after a week again, you know you've got issues and ought to take some x-rays to see if there's arthritis.