I have seen that you can run this tire size on a lift. You may have to pound down the pinch weld as well which means re-working the inner fender cover...not hard with a heat gun.
If you have an '11-newer 4x4 MK forget the CRDSTU lift as paying $700 for 1" of lift doesn't make sense. That leaves Rocky Road, a company with a shady customer service rep & product issues, the only option. Ask around on a KJ board to see how many of their OTT lifts caused suspension damage yet RRO kept selling the lift for years after being told of the problem. This is similar to the fact that their first MK lifts were apparently incomplete and could not be aligned properly...but that didn't stop them from selling them until the poor customers did the R&D to (hopefully) make the lift OK. I personally purchased a different lift from them in 2007 and will not do business with them again. This summer, and against my advice, a buddy tried to order a simple and common TJ spare tire spacer from them and the same old thing happened: he was told the item was in stock ( via phone order) and would be shipped within 2 days. They billed his card. 2 weeks go by with no shipping info being sent. He calls: "Oh we have been so busy we haven't been able to put it in a box to ship it but it is on the shelf and I will personally ship it today." Remember that this is a roughly 5"x5" item...not a large difficult to ship piece. Another week with no shipping info. He calls. He gets the exact same response word for word "Oh we have been so busy we haven't been able to put it in a box to ship it but it is on the shelf and I will personally ship it today." He cancels the order. It looks like once again they lied about having an item in stock when they usually never even stock this stuff anyway... they just drop ship it from the manufacturer. And now 3 weeks later he still has not received his credit back. If you look hard enough for info about RRO you will see that failing to give refunds is just one of their problems. I know this issue happened because, having warned him, he let me listen to his phone calls to RRO over speakerphone when it did not arrive the first time.
That being said the MK has the smallest differential I have ever seen in a real car. Adding bigger tires will only stress it more. It is your jeep and if you are after a poser then maybe it will be OK. If you think to actually gain some performance with the bigger tires and use it off-road afterwards you might want to start with a used & cheap vehicle with real off-road cred like an XJ instead. For what some here have paid for just a lift, tires, front bumper, winch, and sliders for an MK I have a complete & perfectly drive-able MJ that will kill any MK off-road and that includes the purchase price of the jeep. It is your jeep and you can certainly do what you want with it, though.
'91 MJ with some mods
'14 MK without some mods