This is most likely a white balance setting issue, not a bad LCD. The community answer points to your camera being set to a custom white balance in Manual/creative modes. That can give the live view and recorded images a strong green cast if the custom WB reference is wrong.

Try this:

• Press the WB button or open the white balance menu.
• Change white balance from Custom to Auto White Balance (AWB) or a suitable preset.
• If needed, clear/reset the custom white balance setting.

Why it looks normal in Auto: full Auto often overrides many user-selected settings, including white balance choices, so the camera returns to a normal color balance there.

If changing WB fixes it, your LCD is fine. If the green tint remains even after resetting white balance and other shooting settings, then a deeper camera issue could be involved, but based on the answers, white balance is the likely cause.