1. Here's how

When you adjust the shape of the Lumion Terrain, objects that are placed close to the Lumion Terrain will be moved vertically in order to adapt to the new shape.

If you do not want certain objects to move when adjusting the Lumion Terrain, simply follow the instructions below. 

2. Lumion 9.0 and newer versions

Lumion 8.5 and older versions: Please see section 3 below.

Imported Models will not move when the you adjust the shape of the Lumion Terrain. This is by design as you rarely want this object category to move.

2.1: Select the models and click on the Lock object and make it unselectable button:

2.2 The Object Icon changes to red for 'locked', and the padlock icon in Properties is now shown as locked.

3. Lumion 8.5 and older versions

Lumion 9.0 and newer versions: Please see section 2 above.

3.1: Select the models and click on the Context Menu button followed by Transformation. Then set Lock Position to On:

See also:

Video Tutorial: Build Mode: Locking Item Positions