Not really enough information to reply to. The devil is in the details not in evidence.
What is the nature of the power supply circuit between the power transformer and the LED VU display circuit? It could be quite robust and immune from any noise, or it could be flimsy and flaky and passing noise easily.
What kind of bypassing and filtering does the LED VU circuit have internally? It could be a nice quiet neighbor, or a noisy undesirable.
How good is the 5V regulator circuit? Shouldn't it be essentially filtering out any noise coming around from the LED VU circuit?
Does the lack of an arrow suggest that the "Analog Audio Device" is powered independently?
Frankly the most problematic part of the diagram you show is that "audio diode" (whatever that means?)
Connecting a REAL diode to the prime audio path is NEVER a good idea.
Again, since this is only a detail-free block diagram, we don't really know enough to make a useful comment.