I think when Lampard comes, without even taking into consideration the whole debacle that has happened here, people expecting great things will be extremely disappointed.
As a Lampard fan since I was 10 years old I was so excited at the idea of being able to see him play for my club live in person. I didn't get season tickets solely because of Lampard, but it was definitely a large factor. With that said, I wasn't exactly excited to see Lampard dominate the league or even lead the team necessarily. I just genuinely wanted to see him play in person.
After playing the rest of the season with Manchester and coming over in July he is going to be extremely exhausted. His legs were going to begin with, and that is why Chelsea decided not to keep him. Yeah, it was him that rejected the contract, but Chelsea definitely could have offered more if Mourinho was serious about keeping him in his plans.
I believe when he comes over here he is going to have an extremely hard time with the heat of our summers and the intensity of the MLS. Last season with Chelsea the games Lampard played terrible in were the ones where he was hassled and pressed in the middle, his legs just couldn't keep up. I could be wrong, but I don't think the intensity is that much less in the MLS. And do keep in mind that at Chelsea he was often in midfield with players like David Luis, Ramires, and for the second half of the season Matic, all of which were able to cover a lot more ground than Lampard was, and he still couldn't keep up. I'm not sure he's going to get the same luxuries playing for our team.
Now clearly, he is one of, if not the most talented player in the league, but I'm not sure his legs will allow him to showcase it as much as people are hoping. There is no denying his talent for finding the right run late into the box and being an exceptional reader of the game, which works perfectly for him at City, but for our team to fire on all cylinders we need a Lampard that contributes more than that.
I'm hoping to be proved wrong, but thats my hunch.