Conophytum have a resting period in summer, when the existing leaves dry up and form a sheath over the newer leaves - during this time, watering should be much reduced. This process is likely what's taken place, rather than your plant actually starting to die, so don't worry about that. From late summer onwards (end of July), resume normal watering, watering well. If you think it needs repotting, use a shallow pot or pan because they're very shallow rooting and don't need a lot of soil depth. You can repot every two years, but they're usually fine if left a lot longer, they're pretty slow growing, but should be given a low nitrogen liquid fertilizer a couple of times a year if you don't repot into fresh potting medium.
Lithops are usually not watered during winter and watering is started again around May, but if you live somewhere with warm winters, a small amount of water might be necessary during winter occasionally. The advice for potting with Lithops is roughly every couple of years, removing all traces of the old potting compost - this is carried out just before the first watering after winter.
If your plants really haven't grown at all in four years, it may be you're not giving them the right treatment, so its worth reading the information on both plants in the link below - there is an extensive amount of background information on Lithops because there are so many varieties, but the parts referring to growth cycle, watering and potting are towards the end http://www.smale-conophytum.co.uk/grow_conos.htm