When an E-4 calls me "hey" or "hey man" knowing that I am an officer, should I bother to correct him?

During my four years in the Marine Corps I never witnessed such an occurrence. Training and indoctrination from the first day a recruit steps off the bus makes all the difference throughout their career and mission of the branch of service they belong to.

Unless this Lt has personally lowered the professionalism bar for this particular Spc (when off duty, out of uniform, off post, etc.) which he obviously has not as he is asking this question, he should correct the Spc. After having been out of the Army for 39 years, the subordinate soldiers I served with still are inclined to show me respect by addressing me by rank even though I have been telling them we are out and to call me by my first name. They still show me that respect. I guess my question to the LT is why there is a question, by either the Spc or himself, as to whether or not he is due that respect?

Of course you should correct him. If you fail to correct him you deserve the disrespect he is showing you.

Squash that now in no uncertain terms.
The organization works because standards and customs are upheld.
You as a leader set the standards or enforce them from higher.

Sham shield E4 needs put in his place.

Absolutely. But handle it in the chain of an officer. If the soldier does not fall within your command, then get their name and pass it along to that chain of command down to that NCO support chain.

If you’re in an established unit, and you have soldiers who talk like that, there’s no need for benefit of the doubt. The doubt has already been established. Whether it’s the culture of that particular unit or squad or whatever, there’s a problem and probably a big one.

Do not ignore that.

Absolutely. Calm assertive correction, not degrading. Leadership 101

Absolutely! Standards are not what are taught but what is tolerated. Basic military customs and courtesy is a foundation of good order and discipline.

Yes, correct the troop calmly, tell them what they should do, and then point out that the next person may not be do lenient.

“I am happy to be of help, but before we begin, you will address me as SIR or MAA’M as a matter of professional courtesy. This ain’t the Air Force. Off duty doesn’t change that.”

ABSOLUTELY WRONG on all levels. We are in the military on and OFF duty. The rules need to be enforced.