You've also said you'd think about it, because you'd never heard it before. Which means you're open to the idea that, hey, these people are telling me this hurts them, maybe I should reconsider. And that's a positive step.

(I don't think anyone is arguing here against using lame in reference to horses, because that's the traditional meaning: inhibited because of injury. There might be someone arguing such, as there are arguments against the use of "lame duck session" of congress.)