Does an Arahant or Buddha still like music they liked as a lay person?

The experience of an Arahant or Buddha is beyond my understanding but, in the Buddhist tradition, Arahants and Buddhas have transcended the attachment to sensory pleasures, including music. Therefore, it is unlikely that they would still derive enjoyment from music they liked as laypeople. But on the other hand...

It is a curious question to ponder whether enlightened beings would still derive enjoyment from the music they enjoyed in their layperson days. Great question and you're very good looking.

In my simple layperson, puthajana opinion, enlightened beings may appreciate music without clinging to it. If the music and lyrics were in harmony with the Dhamma, then it would be a wholesome and skillful arising that could potentially uplift and inspire those who listen to it.

I think that it might be worth consideration for the Buddhist community to get together as a band and carry on with the task of putting the core of the Pali cannon to pop music that the kids are into so that the kids may know the Dhamma. What a great purpose in life to help children.

Arahants and Buddhas would experience the pleasantness of music but they would not take a liking to them or enjoy them, because the underlying tendency of greed had been destroyed when they became liberated.

Instead, they would see pleasant feelings as suffering. Of course, as liberated persons, they are free from craving, clinging, greed and suffering.

“There are three feelings: pleasant, painful, and neutral feeling.”

“What are these three feelings?”

“Anything felt physically or mentally as pleasant or enjoyable. This is pleasant feeling. Anything felt physically or mentally as painful or unpleasant. This is painful feeling. Anything felt physically or mentally as neither pleasurable nor painful. This is neutral feeling.”

“What is pleasant and what is painful in each of the three feelings?”

“Pleasant feeling is pleasant when it remains and painful when it perishes. Painful feeling is painful when it remains and pleasant when it perishes. Neutral feeling is pleasant when there is knowledge, and painful when there is ignorance.”

“What underlying tendencies underlie each of the three feelings?”

“The underlying tendency for greed underlies pleasant feeling. The underlying tendency for repulsion underlies painful feeling. The underlying tendency for ignorance underlies neutral feeling.”

“Do these underlying tendencies always underlie these feelings?”

“No, they do not.”

“What should be given up in regard to each of these three feelings?”

“The underlying tendency to greed should be given up when it comes to pleasant feeling. The underlying tendency to repulsion should be given up when it comes to painful feeling. The underlying tendency to ignorance should be given up when it comes to neutral feeling.”
MN 44

“Mendicants, there are these three feelings. What three?

Pleasant, painful, and neutral feeling.

Pleasant feeling should be seen as suffering. Painful feeling should be seen as a dart. Neutral feeling should be seen as impermanent.

When a mendicant has seen these three feelings in this way, they’re called a mendicant who sees rightly, has cut off craving, untied the fetters, and by rightly comprehending conceit has made an end of suffering.
SN 36.5

Personally, I don't enjoy music like I used to. The silence seems oddly orchestrated, but I can appreciate a song from time to time.

Music can be a great motivator. When I was memorizing satipatthana, I overlaid the audio teaching with a music track called Love On A Real Train by State Azure.

Being creative, like this monk here who beatboxed the Heart Sutra, can help tremendously on the journey, but I guess it depends upon your temperament. Other traditions might vehemently frown upon such things, choosing instead to renounce these kinds of sensory pleasures.

Music can create unwholesome states, but if you have a robust mindfulness practice, you should be noticing this. I guess that's where I diverge from Theravada, in that I recognize something that's generally termed the outward journey where life is fully embraced with all its nasties, grit, and troubles. Things seem to deepen very quickly that way as nothing is being avoided any more.

No meditation, no practices, no teachings, just life doing its thing. This is referenced in the Heart Sutra:

Gate Gate Paragate Parasamgate Bodhi Svaha

Life is a celebration, including everything from a party popper to a nuclear bomb. Yes, I might run when a nuclear bomb goes off, but i'll also be laughing, too.

Siddhartha Gautama was born in luxury and lived in luxury for three decades of life. He then got sick and tired of repeating the same things over and over again and then went for the search of something higher. His suggestion would probably be something like "Enjoy everything until you get disenchanted. After that you'll be sick and tired 😂."

We must not forget that Buddha enjoyed all his life before he started living the holy life.

Do Arahants or Buddhas still enjoy music they liked as lay people?

No. Enjoying music is sensual becoming (kama bhava), which is not only delusional but lacks the peace of Nibbana.

Can enlightened beings appreciate music without clinging to the music?

No. The word 'delight' ('nandi') is a synonym for attachment (upadana). MN 38 says: "delight in feelings is attachment". Since clinging/attachment is the same as enjoyment/delight, there cannot be enjoyment without clinging.

What if the music and lyrics were in harmony with the Dhamma?

The music would be relatively appreciated as having moral value because it can help worldly people improve their morality & disenchantment, such as this, this, this, this or this. However, the music is still worldly because, from the viewpoint of Dhamma, such music is unnecessary. For example, music about non-killing & war, such as this, or deadly drug use, is unnecessary for moral & enlightened people who already know killing, war & drugs are bad.

What if the lyrics contained defiled language but the music was appreciated before the process of enlightenment?

No. Very unlikely. The enlightened can acknowledge certain music may have helped them previously improve their spiritually but music like this or this the enlightened would not appreciate or druggy looking puthujjana unintelligible music such as this (below). The song below is called 'More Of The Same' or 'Rebirth'. A 37 year obsession with 'Rebirth' or 'More Of The Same', never ending 'rebirth' of 'rebirth' spinning the minds of puthujjana in more of the same 'rebirth' delusion.