Soak the dried cherries in the water for 24 hours. Put the cherries and their soaking liquid in a pan with the thyme and bring to the boil. Simmer for 10-15 minutes until tender. Scoop out the cherries with a slotted spoon and reserve.
Discard the thyme and measure the quantity of cooking liquid.If there is a little over 1/4 pint boil hard until reduced to about that amount. If less, make it up to a 1/4 pint with water. Reserve.
Fry the cutlets slowly in 1/2 oz butter and the oil until just pink at the centre. Remove from the pan, season, and keep warm on a serving dish.
Pour any excess fat from the pan. Add the cherry liquid and sugar and bring to the boil, stirring in any meaty juices from the pan.
Add the cherries and simmer for 1-2 minutes until hot. Turn off the heat and whisk in the chilled butter a few cubes at a time. Pour the sauce over the lamb and serve.