Hmm, I know that they still make 17" or 18" laptops, mostly gaming laptops these days, but ... they're kind of imposing and heavy, and I can't imagine that the larger ones will be all that comfortable, sitting in one's lap. The larger screen in back, makes them want to tip back and fall off of your lap.
A "standard" 15.6" laptop, might be as big as you want to go. Those generally have 1366x768 screens (budget) or 1080P / 1920x1080 screens (a bit higher-end). Some of the extreme / workstation laptops have 4K screens at that size, but those are really pricey. (Obviously, those would have to be used with like 150-200% resolution scaling.)
I kind of second or third the idea of a large tablet, or maybe a mini-PC hooked up to the TV, with a wireless keyboard / mouse ("couch mouse"), and maybe an IR remote to turn on the mini-PC.