Boehner doesn’t have standing. He doesn’t represent Congress. He really only represents a majority in the House of Representatives.
Besides he has other options to check the POTUS. The purse, and impeachment.
That has not been decided in this case. It will be done with a vote of the House. Once they vote on it, it will be the House suing not Boehner. There a good chance that they do have standing.
The flaw in the lawsuit may be in the language of the bill which may be open ended as far as the authority to add administrative regulations to the law.