Is This False Advertising?

In 2021, I signed up for a membership with a very popular yoga studio that has hundreds of locations nationwide. At the time, they sold all their membership rates as “locked in for life”. It was a selling point on their website for years (since changed) and I even have an email from a sales associate saying that word for word.

Yesterday, they email me saying they’re raising the rate by $10/month due to inflation. I called and the best they could do was forward my complaint to their internal team.

Even if this was snuck into the terms & conditions, is this a legal business practice or is it just shady at best? Can I file a complaint with the FTC or something?