Is there a word or phrase for drinking from a cup which is full without lifting it?
I end up having to do this quite often and when I do I slurp. It may not be attractive or polite, but slurping is what the circumstance calls for especially for hot drinks, even if straws are available. Slurping not only allows spill-free drinking, it also cools a too-hot drink (unlike a straw).
Slurp - To make a sucking noise in drinking or eating (OED).