By lip, do you mean that the liner has moved?
What happens when you get what is commonly referred to as a "slipped liner" is that they move inside the block. The leakage occurs when the aluminum bore that the liner is set in develops a crack at some point down the bore, which allows coolant to either enter the crankcase or more likely up and out through the head/block interface.
There are two ways of repairing it. One is what is commonly referred to as a Top Hat sleeve, which is a sleeve with a shoulder on the top that fits into a notch that is machined into the block. For reference, the Rover uses a tapered sleeve. This requires that you fab up blocking plates for the cooling passages, heat the block and then pressure test to look for cracks. Once found, they would need to be stop-drilled and then welded. Your other option is to use the Turner Engineering sleeve, which has an o-ring at the bottom. There is no need to pressure test or weld. If you're unfamiliar with sleeving, there are two typical types, wet and dry. Most heavy truck engines use a wet liner as they need to be replaceable. Most single-bore repairs are done with dry cylinders as the blocks were designed for the structural integrity of full-length material in the original casting, commonly cast iron. With the Rover, you are simply replacing a liner with another and I suppose you could call it a wet/dry liner. Being a design utilizing some of the attributes of a full wet liner, it has the capability of being a "dam" for the water jacket leak. The Turner is also a Top Hat design. The upside of the Turner is that if you get another crack, it won't matter.
Your third option is finding a good replacement block. The good news is that you can re-use the pistons as they virtually never wear. If you move forward with the sleeve approach, make sure your cam bearings are where they should be. They have a habit of moving. I would not invest in a block that has cam bearings that had previously loosened.
You can buy a complete block already sleeved from Turner, but they're not cheap. They will sell you the sleeves, but, as with most things, the end product is only going to be as good as the person doing it. Eight sleeves takes a very competent machinist that isn't in any sort of hurry. That alone just eliminated three quarters of them. A good one is going to charge you a grand for the work.