I am confused by this situation. What is it that the WH said that was a lie, with citations of what they said please. It seems that a series of events occurred..

The GOP leadership in the House decided to invite Netanyahu and sent him an invitation with absolutely no consultation with the WH of this invitation. They did this on what date?
On Wed Jan 21st some member of Boehner's office notified the WH that the invitation had been sent then within something like three hours made the invitation public.

The Jerusalem post reported it thusly
"WASHINGTON -- The White House expressed displeasure with the handling of an upcoming visit by Prime Minister Benjamin Netanyahu to the United States on Wednesday, after the Israeli premier received an invitation by House of Representatives Speaker John Boehner to address a joint session of Congress next month.

Boehner told reporters he did not inform the White House of his plans to invite Netanyahu to the US until this morning. Neither did the prime minister's office.

Aboard Air Force One en route to Idaho, US President Barack Obama's press secretary said that typical protocol for the visit of a national figurehead had been breached somewhere along the way."

I don't see in that anything about the timing of the acceptance in the WH statement. I don't see what LIE you claim was made by the WH. What I do see is an error in the timing in a NYT article about exactly when Netanyahu said yes to the invitation. Where is the WH lie about that timing? The complaint was about the WH being bypassed. And did Boehner admit to that, he certainly did on Fox News. "I wanted to make sure that there was no interference"

If you read the Bernstein opinion story on W Post he clearly indicates that his investigation shows that the invitation of Netanyahu had been delivered long before the WH was informed and the details of the visit had been settled between Boehner's and Netanyahu's offices. Once it was all done and three hours before the public announcement, the WH was informed. Once that happened, then Netanyahu formally accepted the invitation. The WH pointed out that this in not the way such matters are handled and complained. Never did the WH say that Netanyahu formally accepted before they were informed, unless you can find such a citation.

So, again, show me where the White House lied (not where the NYT made an error).