Shutter Lag was very long on the older digital cameras.
Sometimes over two seconds.

The average now is about .5 second.
It can be from 1 second to 0.1 second now, depending upon the camera.

If you use your camera differently, it will not be a problem.
Point the camera at the subject and press the shutter button half-way down.
Spend a second, making sure your shot is properly framed and the horizon level.
Then press the shutter the rest of the way down.

Then the shutter lag will be under 0.1 second.

Shutter lag is caused by the delay the camera needs to focus the lens.
By re-framing the shot, you give the camera time to focus.

Unfortunately the camera makers do not normally publish Shutter Lag information.
You have to dig it out of reviews of the camera by independent reviewers.