That appears to be a very strange problem. I don't suppose you could lay your hands on a spare Cable/DSL Router? If so, you could try plugging that into the main router and then plug your Lenovo Laptop into the "sub-router" to see if it works properly. To do this, it would be necessary for the two routers to operate in different subnets, which would prevent you from "File & Printer Sharing" with computers connected to the main router, if that's significant.
Sony Xperia Z5 review: Hands-on with the phone which the Z3+ should have been