To say something at the top of one's lungs is to say it very loudly, probably by SHOUTING.
The reason Internet writers are encouraged not to use "all caps" (all capital letters) is because it is understood by the native English speaker as equivalent to shouting, which is far too loud for a conversational tone.
Example: Lisa entered the home of her best friend and exclaimed at the top of her lungs, "I'm getting married!!!" Her best friend Janet replied, "That's wonderful!!" in a normal voice.