Your differences you are seeing depend on whether you are viewing RAW or JPG in Lightoom (LR) and what you have LR set up to adjust when you import images. When viewing your images on the camera LCD you are viewing jpg images processed with the settings you set up in your camera. LR has import defaults that will alter what is being imported. Check your Preferences > Presets and Camera Calibration tab of LR.
You can adjust LR for a specific type of shot and make presets to use when importing your images. All adjustments in LR can be used for defining your presets. I'd suggest the LR presets over altering things like the LCD brightness levels. For me - I don't have to worry about what I may have adjusted in my camera to make the image in LR match.