I'm not terribly well qualified to answer this question, but there's probably not all that many other Travel.SErs who have traveled on the road in question, even a good ten years ago...
So. From Mchinji in Malawi across the border to Chipata, the largest town in eastern Zambia, is only about 30 km and easily covered in a day. Chipata has a large Shoprite supermarket for stocking up and a smattering of guesthouses and restaurants etc; Mama Rula's is apparently still there and you could probably do worse than stay there, although it's a few clicks in the wrong direction towards Mfuwe.
Which of these will be your future home away from home? (pic by me)
From Chipata to Lusaka you're on the Great East Road, which is the main highway connecting Lusaka to all points east. There is thus a steady stream of trucks, buses etc and the infrastructure to cater for them. That said, this is the African bush and there are no towns of size along the way, so you're not going to find anything approaching Western standards, but if you're OK with nshima and grotty rooms with a fan if you're lucky, you'll survive. Bridge Camp, around the halfway mark near an otherside pretty desolate stretch, is apparently still there as well.