Is this quote true? On the face of it, it's no more of a lie than Sarah Palin saying she put a state plane on ebay--she DID, but it didn't sell as a result of that.
The point in the earlier case was that it showed Palin's unconventional and clever way of dealing with the situation, not that ebay is a great place to sell and airplane. In this case, it seems Perry was showing that he was lobbied by this woman. If the quote above is factually true, I don't see that this is the end of the world--it's just politics. And these are politicians.
I guess some people are upset because they thought he was saying she lobbied him before he signed the EO, even though he never said that and was just trying to give a face to the reason one would support what he did.
So long as she lobbied him about it, that’s what he said, so it’s not a lie. She may be the reason he initially fought the legislature when they opposed his EO. She was lobbying for him to defend his EO against their attacks. After all, people have attacked him for that as well.