By loudspeaker he most likely is referring to the internal speaker in the phone rather then a third party speaker system that's connected wirelessly to the phone.
Most cell phones have the internal speakers that amplifies the sound that's equal to the speakerphone option on most landlines (though not as loud due to the speaker's small size).
As for why there is a lag, I couldn't guess. Maybe you dropped your phone one too many times. Is it an old iPhone?