I have to say that I am not familiar with carpal laxity syndrome so I have just looked it up. There is an explanation here
. Apparently it is due to "exor/extensor muscle imbalance and that it "frequently develops following a change in diet, especially when the diet is unbalanced, over-supplemented or of poor nutritional quality."
Management-wise they say that there are "two key aspects to management are feeding a commercial balanced diet
and exercise on non-slippery surfaces, such as grass.
In view of this management strategy, I can see why you are keen to feed a good diet and I would totally agree that it is important to get it right. TBH I would be looking at some of the higher rated products such as Applaws, Eden, Evolution, Orijen etc. Some of these are for all life stages so don't be worried if you don't see a puppy version. The only difference between puppy and adult is that the former has higher protein levels but the better quality products have this anyway. If you purchase a good quality kibble you should not need to supplement with wet food.
By using the Dog Food Directory here
you could narrow the search down considerably. Using the filters on the left side of the page, select the following:
Type of food - dry
Food properties - natural, clearly labelled and grain free
Rating - adjust the slider to 4 -5 stars
Avoid ingredients - all red and all cereals.
This brings up just four pages of good quality products and you should find something suitable, and to suit your pocket within those pages.
In the article it says that the prognosis is good and I do hope that this is the case with your Lurcher puppy. Well done for rescuing the poor mite and I hope that he is soon well again with your care and support.