Think of an LCD screen like a TFT monitor (essentially the same thing) These work in pixels. A typical 32" LCD screen will have say, 1366x768 pixels. This means it can do 720p, but not 1080i/p.
Now all CRT TV's have 576 lines, no matter of size. Which is why 14" CRT's look sharper and crisper than 36" CRT's. I have a 36" CRT and I presonally think it looks the bollocks with a strong digital TV input, ie Freeview, or a DVD. My brother actually thinks my CRT looks shrper, crisper and faster than his 32" LCD (LG) and of course the black levels are FAR superior (there isn't a plasma or LCD on the market that can touch CRT for speed/refresh rates or black levels)
Going back to LCD's, a 32" with 768 horizontal pixels will show in 720p format, so a 576 line picture has to be enlarged to fill 720 lines.
As with anything, if you go bigger, the pixels become bigger. The ammount of lines stay the same (if comparring like to like 720p ratios) just the lines get bigger. So the bigger you go, the bigger the picture is replicated. and thus you will lose quality. A 26" LCD will look sharper than most 40" LCD's....