Juventus has reached the Coppa Italia Final, which is supposed to be played 7 June, 1 day after the Champions League Final. Playing either one of those the following week would conflict with Euro 2016 qualifying.
First of all, there is no way in hell UEFA would switch the CL final so Juventus can play a Cup match!!! The actually backup plan is to hold the Coppa Italia Final on May 20th should Juventus reach the CL Final. This might cause some logistic issues as the change will only be known 1 week before hand (CLSFL2 is on 12-13 May!)
Lazio will play in the Coppa Italia Final, and if it's May 20 that's four days before Lazio hosts AS Roma in a big Serie A game that could decided second place. I'm assuming Lazio would rather not have a midweek game and have to play AS Roma with less rest than AS Roma would have, not that Lazio has any say in the matter.
More importantly it would conflict with Copa America. So pushing back the Coppa Italia is not an option. Not even by 2 days.
Wrong Timing. Serie A needs better management even if they thought none of the Teams in the league would have made the final they could atleast considered travelling fans too.