My cat does the same thing. Hes just a lazy cat. He's also tall and doesnt like to strain himself bending down to eat (I can't raise the bowl since my other cat is shorter and will knock it down if she doesnt reach) so he lays down. If your cat is tall or fat like mine, thats probably why
My cat tries to get as low as he can to drink, laying down sometimes, and sometimes not, but almost. He's neither fat nor lazy and he has been sneezing for a couple years, and getting worse. He has clear runny snot. I think the laying down has to do with clearing his airway, so he can breath through his nose while he drinks.
Is it a fat cat. Mine lays down too, and I believe it's out of laziness and it's more comfortable for him to lay down than to put the weight on all four paws. I go over every so often and stand him up as he's eating.