This may be memory bias again, but (speaking more broadly than just Cliff Lee) I seem to remember us handling aces pretty well over the last few years. (Can't speak for the second half of last year because I was one of the pink hats who stopped paying attention right around when they lost their 115th game.) I'm way too lazy to look up the stats, but I wouldn't be surprised to see that we hit aces pretty well. I mean, no one hits aces really well or they wouldn't be aces, but I seem to recall us holding our own at least against the Verlander/Sabathia types.
You may now destroy my feeble memory with actual stats if you are so inclined.