Xbox 360 on Widescreen LCD HDTV: Zero Risk of Damage
No. Connecting an Xbox 360 to a widescreen LCD HDTV is completely safe. The console outputs standard HDMI/Component/VGA signals that all modern TVs are designed to accept.
Things to Check for Best Experience
Aspect ratio: Set Xbox 360 → Settings → Display → Widescreen (16:9) to match your TV.
Resolution: Choose 720p or 1080i/1080p (if your model supports it) for sharpest image.
Overscan: Some HDTVs crop edges; enable "Screen Fit" or "Just Scan" in TV picture settings.
Ventilation: Keep the console horizontal with 6+ inches of clearance—overheating harms the console, not the TV.
No electrical, signal, or physical incompatibility exists. Enjoy your games!