I just realized that I haven't yet addressed the acclimation issue here directly but it is something all of us have good or not so good experiences with.
Obviously not every Lithops or other succulent we grow is the one we grew from seed. A lot of them were acquired as seedlings, cuttings or adults. You probably also have noticed that the plants you grew from seed are stronger and healthier and don't die that easily. They hatched in your particular conditions and are used to the care you give them. They accept what they get without complaining while the plants we receive as adults first need to learn and get accustomed to the new situation they find themselves in.
If you receive your new plant in the mail it's normally "bare-root" and you have no choice but to pot it. But also if you buy one in the local shop or at a nurcery, in its own pot and substrate, the first step should be re-potting. Even though it appears to not be helpful in terms of "easy transition" it's still important to 1) check the roots and 2) make sure there are no bugs. In case of a purchase from a local flower store I would highly recommend to "brutally" wash the plants under the tap until all the bits of soil are gone. It's okay if they lose most of the thin roots while you do so - they grow out very quickly.
Now that you've potted your new (dried after washing) plant into the dry soil mix of your choice (pure pumice for me) you're all excited and looking forward to seeing it flourish. After all you've done everything right and the conditions at your place are also right for the plant as you proved on your other similar tenants.
But that's when acclimation comes into play.
First couple of months are critical. In case of Lithops you might first say the plant made it after a timely and successful regeneration which can be a year after purchase. Also, in case of Lithops usually the only way to detect that something went wrong is to find the plant dead one day. But if you see that the plant doesn't drink after the first watering (at least a week after transplanting) it isn't necessarily a bad sign. With the first watering the roots are just being reactivated and after the second and third watering they should start to react to water properly. Wrinkly state and no reaction to water is from my experience a typical acclimation behavior. The other and more dangerous one is rotting. Even in a dry substrate and minimum disturbance a plant might just "freak out". There's nothing you can do for Lithops if it happens. It's bad luck. With other plants that have more than 2 leaves at a time it's time to act. Dig it out, cut off all the rotting leaves and let it dry without substrate. Pot again only after you made sure that the rotting stopped and it doesn't lose any more leaves.
I currently have this scenario with my recently purchased Crassula 'Coralita'. Quite some of the older leaves have rotten off in a day so at the moment it lives upside down. No further damage since two days but I'll wait for several more days before I pot it again just to make sure. Patience is the key :)
Please share your experiences in the comments! I'd love to read your thoughts on this matter.