Based on Vietnam War casuality information provided by the National Archives at http://www.archives.gov/research/military/vietnam-war/casualty-statistics.html it's not possible. Various others have reparsed the official data (e.g., http://www.americanwarlibrary.com/vietnam/vwc4.htm)

If 806 O1s died during the conflict. Roughly a third of those were direct combat related causalities, and slightly under 30% of the total deaths occurred in 1968. Any way you cut it, that's a far lower lower number than could support such a statistic.

Note there's a couple caveats like posthumous promotions which might muddle the waters, but I still don't think you could get close.

EDIT: MORE ACCURATE NUMBERS (again, from NARA):

105 Second Lieutenants that had been in rank for under one year were killed (or died of wounds) in 1968. Additionally, 16 individuals who died as Second Lieutenants having served under one year were posthumously promoted to 1st LT.

To see the proportion of academy vs OCS vs ROTC deaths would take some original research

Could someone also clarify what is meant by "life expectancy" in the context of war? The British seem to have calculated such a number for pilots during WWI.
https://books.google.com/books?id=Y82WHKm2QBYC&pg=PA40&lpg=PA40&dq=life+expectancy+british+pilot+wwi&source=bl&ots=Fq24DrYJh_&sig=gH80den5zvThJ9NZcYLAHFzdOc0&hl=en&sa=X&ei=D9fkVMHLM8LkoAS_zYGQBg&ved=0CB0Q6AEwADgK#v=onepage&q=life%20expectancy%20british%20pilot%20wwi&f=false

My first instinct is that this number is meaningless because the number keeps getting bigger as the survivors get older ... instead, I have the impression that these statistics apply only to those people who ACTUALLY DIE.

So, if 100 pilots go into battle and 50 are killed at the first minute while the rest survive, I think we would say "there was an average life expectancy of one minute ... among those pilots who died in the battle." The same would be true if only one was killed and 99 survived. Right?

This data isn't likely available without digging deep into Army and Marine Corps death records and action reports. You'd have to narrow it down to the day and time of death, cause of death due to combat, as well as the fact that the question asks about being dropped into a hot LZ.

And even then, the question of how life expectancy is defined matters - is it the average time a second lieutenant lives upon touching down in an LZ before on average, one is killed?

However, even a cursory look seems to suggest the saying is infeasible. According to data pulled from http://thewall-usa.com/, and from /u/aelfric 's post on 1968 deaths as well as /u/death_bag 's post on O-1 deaths in country, the quote for life expectancy of a second lieutenant dropped into an LZ isn't likely to be anything close to 16 minutes.

In fact, that data shows that 233 O-1s were killed in all of 1968 with 143 being Army O-1's. 1 was Navy, 1 was Air Force - both of whom were lost in fixed-wing aircraft. Thus with zero Coast Guard O-1 deaths, we have 98 Marine Corps O-1s killed that same year.

Note too that 575 O-2s were killed that same year - and even taking out Air Force and Navy O-2 deaths which skew heavily towards aircrew, we have 527 Marine and Army O-2s killed that year.

So on paper, by the casualty totals, there weren't all that many O-1s in Vietnam compared to O-2s and O-3s.

Also, with 231 O-1s in the Army and Marine O-1s killed in 1968, that averages out to 0.6 killed per day. With 16,899 American deaths in Vietnam that year, O-1s accounted for an average of 46 deaths per day, O-1s only accounted for 1.3% of all deaths.

Now, I don't have a breakdown of the ratio of 2nd Lieutenants to all those who served, but the closest data I can pull up right now is from Army information from WW2: link here -- the actual PDF with all this data from the Army report after WW2 is missing in my google searches, but this is the same data.

A total of 44,757 second lieutenant casualties (including 27,546 Air Corps second lieutenant casualties) out of a grand total of 936,259 battle casualties. Removing the Air Corps casualties, which is heavily officer centered (and for which 2nd Lts. account for over 24% of casualties), we see that in WW2 2nd Lieutenants accounted for 17211/823493 Army casualties, or around 2% of all Army battle casualties.

In addition, this table shows that 14,437 Army second lieutenants were listed as KIA of the 189,696 total Army KIA. Again, removing the Air Corps' 10,845 second lieutenant KIAs - which is a shocking figure in itself - we get 3,592 non-Air Corps 2LTs KIA.

That accounts for just 3592/144911 = 2.48% of all Army KIA in WW2.

While it's hard to compare the two wars given changes in the Army's composition in the 20 years in between, 1.3% in Vietnam vs 2.48% in WW2 of all KIA, it does seem to suggest the saying that the average 2LT in Vietnam having only minutes to live in even their first engagement is a gross exaggeration.

EDIT: Found 2012 military demographic data to compare.

At its peak, the US had 549,000 troops involved in the Vietnam conflict

Per this link, for 2012, roughly 17.2% of the US armed forces are officers, or roughly 4.8 enlisted per officer (5.24 if we don't count warrant officers).

Section 2.04 performs a breakdown of the ranks - roughly 1.8% of the entire military is an O-1 (Army 1.7%, Marines 1.3%). Another 2.2% of the entire military is an O-2 (Army 2.4%, Marines 1.9%) and 5.4% are O-3s (Army 5.2%, Marines 3.5%).

Yes, the US military has changed its organization since WW2, but the casualty breakdown of the Army in WW2 mirrors those %'s fairly closely with 2LTs accounting for 2.5% of all non-Air Corps Army deaths in WW2.

Going off of that then as a basis for an estimate, with 549,000 US troops involved in Vietnam and estimating O-1s, we have anywhere from 5,500 O-1s (if we assume 1% of the military was O-1) to 11,000 O-1s (if we assume 2%).

Needless to say, the % of 2LT's that died in action in 1968 was a small percentage of the overall that served and further calls into question the idea that 2LT's died at such rates.

If anyone wants to start playing with numbers:

231 2LT were KIA between 1/1/1968 and 12/31/1968 according to http://thewall-usa.com. I didn't dig through the data to determine which were actually killed by hostility rather than accidents or illness.

One USAF 2LT was killed in '68 but he was not "dropped into a hot LZ".

What constitutes "hot" -- one farmer with a bolt-action Mosin? A booby-trapped LZ but no enemy combatants?

I'm wondering where you've seen this cited? I've heard this statistic too, but only in the film Rules of Engagement.

Wouldn't this statistic mean that, in any hot LZ in the first 16 minutes half the Lieutenants would be dead?

This was in a theater where firefights could go on for hours, with all the concealment and cover available. Per rmosquito below, there were 801 O-1 deaths over all 9 years of the conflict. Approximately 7 deaths a month, divided among all the combat platoons active there. Either combat in Vietnam was far less frequent than most believe, or this is a made up statistic. Also, nobody seems to have a source.

Seems very unlikely.