My DS never wants to do anything and moans about going out, but enjoys himself when he gets there. He is just something of a homebody, I think.
After school he runs straight to the laptop for permitted hour of gaming, then he just messes about in the house. He does card tricks endlessly , re-reads comics, whittles sticks, climbs over the banisters, takes things apart, finds forgotten treasures in his bedroom, practises faces in the mirror, tries to levitate like Dynamo, and just hangs about, until dinner or piano practice is forced upon him.
Your DS may well be missing his friend, but I don't think his reluctance to do anything is necessarily a symptom of that.
I've just started taking DS to coder dojo at weekends, to try to increase his circle of friends and acquaintances before secondary school, as his two closest friends are likely to go elsewhere.
does your DS do sport outside school as well?