Why is there a time lag when I put my iPhone on loudspeaker?

If by referring to being on loudpeaker do you mean you're connecting using a Bluetooth device?

I mean, I press the 'loud speaker' button so I can hear them from the phone speakers on a higher volume and reply to them without having to hold the phone to my ear.

Assuming that it is not how the loudpseaker connects (with Bluetooth), then the loudspeaker connection just has a built-in time lag...it's the nature of such phone-network-to-loudpeaker communication devices.

Not much can be done to my knowledge..other than changing to a different network. for example....using Verizon to connect the phone conversation versus a slower network..say Nextel.

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?

Here's a thought. When you switch over your Iphone to speaker-phone...make sure the room is quiet (no background nosie...TV etc.) when the other person talks..and that no one else is talking at same time.