Similar to the E-2 question, how would you react to a young 2LT who is being unprofessional with a strong sense of entitlement?

If at all possible correction should be done off to the side and as low key as possible and most importantly with a witness to back you up. Otherwise it might be best to avoid saying anything. Remember; Always pick the time and place of your battles and prepare the battlefield.

Hmmmmm....how do I put this without offending both sides. In another life, I was once a former US Army Mustang (Officer that was once enlisted). I have seen it from both sides. The LT was definitely wrong but keep in mind two wrongs don't make a right. I know this is offensive to some people, especially those NCOs who are looking for an opportunity to ride rough-shod over an officer. It can be a hard thing to imagine but you have to use tact in dealing with everyone, seniors and subordinated alike. Just remember this, there is no such thing as disrespect to a NCO from a commissioned officer. However, the opposite is true. It is true that regardless that the LT was wrong. I have found there are other ways to address issues.
I know it makes some people angry that the LT walked away but here is my question to those who it makes angry, why? You did the right thing and there is no reason to sink to an unprofessional level just because someone else is acting unprofessional. However, you can always use tact. You could simply walk up to the LT and ask them what they are listening to? Or even say something like, “Sir, the post commander occasionally comes in here and I know you are enjoying the music but I don’t want to see you get jammed up.” I think that might go allot farther.
Correct the LT and walk away. If he doesn’t listen then he is acting foolish. I have known allot of NCOs who had to deal with stubborn and foolish junior officers. The solution is that you have to let them fall on their face once or twice before they start to learn. However, if you outrank him then that is a different issue.
Here is why I am saying this; there was a SFC who told me something similar. However, I wasn’t at the commissary. I was in uniform and I wasn’t a LT but a CPT. However, I was sitting in a mobilization center waiting for a bus to go back to war in Iraq for a third time and I was talking to my loved ones before I left out while the phone was charged. I knew it wasn’t correct but I could not hear unless I used a headset. Sorry but I have heard allot of large booms in my career. The SFC was correct but it was the way he did it and that’s what made it dead wrong. He should have used tact and disrespecting a commissioned officer is one thing that will jam an NCO faster than anything. It doesn’t matter how right you think you are when you step outside the rules then you are just as wrong. By the way, the SFC wasn’t deploying and was staying stateside just like he did for most of his so called “illustrious career.”

Get his name and unit.
Meet with a senior officer in his chain in a professional/work environment that day or the next and politely explain what happened, express the same concerns with that 2LT's failure to meet standards and add that the response was a more damning example of PPP.
In a GOOD organization, I probably wouldn't have to say anything else or even ask something odd like, "so what are you going to do ...?" I would expect - hope - to be almost interrupted by, "Thank you. I will have a word LT X and ensure corrective measure are taken."

I'd also keep an eye peeled for this guy for either further transgressions, better bearing, or attempts at retribution ...

You mean like the West Point grad who displayed a pic of communist/terrorist/murderer Che Gueverra on the t-shirt he was wearing under his uniform. He had the picture taken after his graduation ceremony, added it to his social media for God's sake and yet was commissioned anyway.....as far as I know he is still "serving"......why don't we address stuff like that or a requirement for male cadets at another school to wear red pumps so they can know how women feel who "have to wear pumps". I think we all know that women are allowed to wear flats while in Class A's or B's. They wear pumps because they choose to do so.
The commissary question is a non starter....the military is too PC today to seriously address something like a butter bar wearing headphones in the commissary....

Well, if I am senior in grade and his response is anything but to remove it and apologize, he finds out "Yes, Virginia you really can fill out a charge sheet on an officer." If I am the same grade or junior, officer or enlisted, I find an officer senior to him and refer it to that senior officer. If I am a junior enlisted man and he's really an ass about it, I find a Sergeant Major, and then quickly scoop up small children and young dogs, then look for a bomb shelter.

I never had a problem with a junior person correcting me on issues. May not have liked it all the time, but I also realized that it takes balls to tell an officer that they have a problem. I also knew that most times, the junior had more experience than I did... If the Officer does treat the junior disrespectfully, that is never right, and they should be reported.

wait for him to figure it out/ an laugh behind my hand

For one,unless he approached me i would ignore him
Second thoze boot lt's are more trouble than their worth and can cause you more misery than you want so i would just let it slide because most likely a higher up will confront him.

Off the top of my head, if you're a senior NCO or higher, correct him. If he gives you attitude, chew his ass. Being a LTC with 5 years of enlisted service prior to OCS, I understand and appreciate when anyone, especially a senior NCO or higher, respectfully tries to give me a correction, and I'll gladly say thank you.
But if this is another junior officer who thinks he's been coronated rather than just commissioned, give him the appropriate attitude adjustment, along with a message to his next higher officer.

He wouldn't dare say that cause I'd snatch it right off his head.