Did Cohen lie about the Trump Moscow Tower project?

Obviously yes.  He testified in August 2017 before the SSCI and HPSCI about his involvement with the Trump Moscow Tower project and in a letter stated three things:  "First , Cohen stated that the Trump Moscow project had ended in January 2016 and that he had briefed candidate Trump on the project only three times before making the unilateral decision to terminate it. Second, Cohen represented that he never agreed to travel to Russia in connection with the project and never considered asking Trump to travel for the project. Third , Cohen stated that he did not recall any Russian government contact about the project , including any response to an email that he had sent to a Russian government email account."  Mueller Report, Vol I, pg 195.

All three of these statements were lies. "Each of the foregoing representations in Cohen's two-page statement was false and misleading. Consideration of the project had extended through approximately June 2016 and included more than three progress reports from Cohen to Trump. Cohen had discussed with Felix Sater his own travel to Russia as part of the project , and he had inquired about the possibility of Trump traveling there- both with the candidate himself and with senior campaign official Corey Lewandowski. Cohen did recall that he had received a response to the email that he sent to Russian government spokesman Dmitry Peskov-in particular, that he received an email reply and had a follow-up phone conversation with an English-speaking assistant to Peskov in mid-January 2016. Cohen knew the statements in the letter to be false at the time, and admitted that he made them in an effort (1) to minimize the links between the project and Trump (who by this time was President), and (2) to give the false impression that the project had ended before the first vote in the Republican Party primary process , in the hopes of limiting the ongoing Russia investigations." Mueller Report, Vol I, pg 196.

Cohen was sentenced to two month in prison for these lies, to run concurrent with a 36-month sentence imposed for other counts.

Now the big question: Did Trump tell Cohen to lie?
Buzzfeed ran a story on January 17, 2019 claiming that Trump told Cohen to lie about the Trump Moscow Tower project. "A proven effort by Mr. Trump to pressure a witness to commit perjury would be one of the most damning revelations so far in the investigation into Russia’s attempts to sabotage the 2016 presidential election and could be the cornerstone of a case that the president obstructed justice to keep investigators at bay."

However, this story was false, and Trump did NOT tell Cohen to lie.  Mueller said it himself.  In a rare move, Mueller stepped in to dispute the accuracy of the Buzzfeed article.  "The special counsel investigating Russian interference in the 2016 election disputed on Friday ([1/18/2019]  a report that said President Trump had directed Michael D. Cohen, his longtime lawyer and fixer, to lie to Congress about his role in negotiations to build a skyscraper in Moscow. “BuzzFeed’s description of specific statements to the special counsel’s office, and characterization of documents and testimony obtained by this office, regarding Michael Cohen’s congressional testimony are not accurate,” said the spokesman, Peter Carr."
https://www.nytimes.com/2019/01/18/us/politics/buzzfeed-cohen-russia-tower.html

While I am at it, let's talk about Charge 11:
K. Trump called Michael Cohen a "rat" after he "flipped".

Trump did call Michael Cohen a rat because he is a rat. Nobody told him to lie, and he can blame no one but himself. So this charge does NOT support obstruction of justice.