Our house has kissing lanais. Our neighbors eat most meals on their lanai. We will be busy doing whatever it is retired people do when all of a sudden we hear her setting the table. We laugh and say lunch time.

Tv's in kissing lanais are rude
 

In my opinion Tv's and loud music in kissing lanais are rude. With all the rules in the villages you would think this one would have been added.
When we rented last year one of the houses behind had speakers wired in the lanai and we could hear their music blaring out anytime they were home even though they were very seldom on the lanai.

But I might try giving the neighbor brochures or printouts from the net for wireless speakers with volume control that they could set right by their chair it is what I have as I too am a little hard of hearing and it allows me to hear without having the overall volume up so loud.
Also a universal remote would turn off their set, when no one is there and they have left it running. The distance they work is quite far and you could probably stand in your lanai and adjust both the volume or turn off their set but that really would start a war.

Report to Community Watch to see if that helps.

A karaoke machine? I think that might cause some fights.

We had a neighbor way down the block have a Bunco
night out on their lanai. The yelling and screaming (at the top
of their lungs) went on for over 3 hours.
It went on from about 6 until after 9.

I finally heard the next door neighbor blow his top.

I agree. Even if you live on a golf course or pond, you still have neighbors on either side, 20-30 feet away, depending on your kind of house. A loud tv on the lanai would be just as inconsiderate to people on either side.

Who doesn't have a Karaoke machine?