It appears that the loud clicking noise in your LG dishwasher (model # LDTS5552D) is likely associated with the completion of the cycle and persists until the door is opened. The issue may be related to the door latch mechanism or a component involved in the cycle completion process.

To troubleshoot, check for any visible obstructions around the door latch and ensure that it is functioning properly. Additionally, inspect the dishwasher's interior for loose items that might be causing the noise. If the problem persists, considering attaching the audio file could provide more insight into the specific sound, aiding in a more accurate diagnosis.