This IMO, would be a great partnership.
Although one thing does concern me, does Andy have the personality to have a hard taskmaster as coach?
Beggars can't be chosers, and I think Andy has reached the stage where, if he is really serious about his career, which I still think he is, he no longer has the option of being 'picky'. I suspect Lendl may have been following his fortunes for a while now. He's seen what he was like at the AO and what he's been like since, and has decided to strike while the iron was hot. Murray was screaming with rage and frustration after the Bogolomov match.
I like Lendl's work ethic - "If I don't practice the way I should, then I won't play the way that I know I can", something which I think would appeal to Andy. And you're right about their personality similarities, as this photo of Lendl off court shows -
I'm not so sure that we could be looking at a Murray/Gilbert situation again. Andy has matured a lot since those days. Then it was stroppy teenager versus middle-aged man who were forced to spend 24/7 in each other's company.
However, Andy apart, other things will have to be ironed out - not least Corretja's position. If this partnership does come into effect, I can't see it happening until Wimbledon, Corretja being Andy's clay-court adviser.
Lendl may not have coaching experience, but didn't so many of us agree at while ago that a multiple GS winner would be an equally good option?