I really don't run into the problem of having Jirachi Lysandred up and taken out for the game that often (and I play Jirachi in next to every deck), but when it does happen I just remember all the times it has saved me from drawing dead. It doesn't happen that often either because I discarded Jirachi, haven't played it, or my opponent has used one of the many other ways to win the game. I could lose by not getting a Megaphone, not waking up from a Laser, or not getting Lysandre fast enough while my last healthy Pokemon is chipped away at.
Really, Jirachi is a high risk-high reward kind of thing, but I feel that you gamble harder if you don't play it. My favorite example is the "getting good draw support on the first turn" one, because that's one of the most important times to get a Supporter. If you have 4 Juniper, 4 N, maybe 3 Skyla, and a Computer Search(12 total cards with access to good draw) you will start without any of those about 19% of the time. However, adding JirachiEX, you get maybe 4 more cards that can access draw on the first turn if you also play 3 Ultra Ball(16 cards with draw access), which means you only start without anything good about 10% of the time. On top of that, playing 10 Basic Pokemon besides Jirachi means you only have to start with it around 3% of games.
If that's not reason enough to play Jirachi in most every deck, then I think it should at least be used in decks that use AZ, like Fairies and Bronzong. Your opponent then has a very small window of opportunity to Lysandre for an easy two prizes, and after you pick Jirachi up, you could even use it again later.
Silent Lab will hurt, but only if it ends up being played a lot, which I don't really think it will.