Should a 2LT salute a 1LT?

Yes!

I'm a coastie, but I was in the army for 9 years, had three platoons, and one company command.  I can't believe that this topic has produced such a volume of discussion.  Aren't there bigger issues in the army worthy of debate than whether a 2LT salutes a 1LT?  It's been the tradition for decades, and if it hasn't caused a breakdown in the chain of command after after all that time and three wars, it probably isn't going to do so in the future.  As we used to say, honor among lieutenants is like honor among... well...ladies of the evening.

I agree with most who have posted here. A salute is a courtesy and sign of recognition of achievement to a senior. Not to salute a senior would be akin to walking past someone without a greeting. This is not how I was raised, and certainly not what was expected when I was in the service. On a personal note, it's a bit disappointing as well. Nowadays people seem so in-tune with the latest technology, that we've lost the most basic of human courtesies. My hope is that in the military, this time honored tradition will be preserved.

I agree with what most have said.
A salute is a military courtesy as a sign of respect and recognition of achievement in the military. Not to salute a senior officer is akin to passing someone without a respectful greeting. This is not how I was raised, and certainly not what I saw when I was in the service. It's also a bit disappointing on a personal level ... the world seems so atune to technology that we've lost some of the most basic of human courtesies.

Out of respect they should but I also see both sides of the coin.  Obviously someone that is not an O-1 should offer a salute.  It really depends on how much it went to their head in my opinion.

"What if a 1LT walks towards a CPT and a 2LT walking together? Should the 2LT not give the salute to the 1LT even though the 1LT was primarily saluting to the CPT? Answer: the 2LT salutes with the CPT and the 1LT salutes first, not because of the lack of respect from junior LT to senior LT."

Yes. Always salute a senior officer. This should NOT be a question that someone contemplates. 

Allow me to ask another question. What is the big deal about rendering a salute? Is it a hardship to raise your arm and render a sign of respect to another service member? Personally I say salute show respect and move on. Odd as it may seem, I've seen enlisted salute other enlisted as a sign of respect (notably one of my Drill Instructors saluted another Drill Instructor from another company out of friendship and respect). Should it be done according to regulations yes, but the reality of the world is that although something may be in the regulations it isn't always the end all be all of the exact way business is conducted.

I say do it unless otherwise directed, and if you're a 1Lt saluted by a new 2Lt, return the salute and chuckle about it to yourself later in private. No harm done.

I'm not sure what the issue is, Sir. To me, this is like asking, 'Should a Lt. Colonel salute a Colonel?'. Just as there are several difference between a Light and a Full Bird, much of the army recognizes differences between a Lt. and (excuse the phrase) a Butter Bar. But regardless of opinion, regulation clearly states the proper procedure. And besides, it's actions like these that create controversy. If some witnesses the failure of an O-1 to render a salute to an O-2, they might immediately see it as an act of disrespect or a general lack of respect for traditional customs and courtesies by both officers. Rule of thumb for me in training was, "When in doubt, salute. No one ever gets smoked for saluting."