Solution

This can be achieved by creating a copy of the appropriate Base map in Studio and setting the Scales so that it only includes the single scale that you’d like to display the map at and then hiding the Zoom buttons.

Step-by-step guide

Create a copy of the Base map you wish to use for your Lite map.
Set the Scales under the BaseMaps > Details so that it only includes the single scale that you would like the map to be displayed at.
Add the BaseMap to the MapSource that you are using for your Lite Map.
Add the following CSS to your web page to hide the Zoom buttons.

			/* Hide the zoom controls for this map */
			#atZoomControls {
				display: none;
			}

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