Boris Johnson Didn't Lie
Boris Johnson did not lie to the queen. Brexit is not the only thing going on in Britain. There are other issues that need seeing to and the ending of the parliamentary session was an opportunity to give those other issues a platform and a place on the legislative agenda.
As a new prime minister, Boris Johnson also needed to hold a Queen’s speech. 47 days had passed since he took office and he had still not held a speech. This was highly irregular and a break with leadership conventions.
If He Did, It Wouldn't Make a Difference
Even if he did lie to the Queen, that wouldn't make the prorogation unlawful. Firstly, none of the treason acts (1351, 1702, 1708, or 1848) declare that lying to the monarch is a treasonous act.
Secondly, the Queen, at this stage, is merely a rubber stamp. She does not intervene in politics and would grant her prime minister a prorogation at his request, regardless of the reasons. Whatever Boris Johnson's motives for the prorogation, the very fact that she approved it makes it lawful.
Finally, even if we accept that lying to the Queen about his motives for prorogation is illegal, it would also be on the court to prove that Johnson lied to the Queen. Given that the conversation only took place between Boris Johnson and her majesty, and she isn't going to testify, we will never know whether he lied or not.