Nothing to offer on the threes but for those who don’t know… the song is If I should Fall From Grace of God by the Pogues, sung by Shane McGowan (sans dental work). 
Is it related to the idiom “go down for the third time”?
The lyrics’ writer (and singer) IS Irish, so he probably wasn’t fooled by his own accent.
Additionally, the Irish accent makes the “th” sound a “t” or “d” sound–not the other way around. I.e., “threes” becomes “trees” with an Irish accent, but “trees” never becomes “threes”.
I’m hoping that this thread has come up for the third and last time. But I guess zombies don’t drown, do they 
monster_sausage, this is your first post. What you have done is found a very old post (started in 2007, revived in 2011, and now again in 2012. This is called a zombie (there will be zombie jokes), and some of the participants are quite possibly no longer present on the boards. In general, it is worth checking the date of the post you are responding to, and starting your own thread on the topic in question if it is fairly old.
As for my comment - many lyric sites on the internet are public contributions, and do not always reflect what the songwriter/singer may have written/recorded (I have seen some pretty serious howlers when finding songs for my own playlist). And the thick brogue and toothless enunciation of Shane McGowan is particularly difficult for those not familiar with Irish speakers. Finally, the similarity of the irish pronunciation of tree and three are well attested in humour - which I indicated by my use of the 
[FOGHORN LEGHORN]That’s a joke, I say, that’s a joke, son[/FOGHORN LEGHORN]
Welcome to the dope, we do hope you’ll enjoy your stay, but spend a bit of time lurking until you get a better feel of how we work, and your interactions will be much more enjoyable and productive.
Si
[quote=“si_blakely, post:24, topic:407968”]
I’m hoping that this thread has come up for the third and last time. But I guess zombies don’t drown, do they
monster_sausage, this is your first post. What you have done is found a very old post (started in 2007, revived in 2011, and now again in 2012. This is called a zombie (there will be zombie jokes), and some of the participants are quite possibly no longer present on the boards. In general, it is worth checking the date of the post you are responding to, and starting your own thread on the topic in question if it is fairly old.
As for my comment - many lyric sites on the internet are public contributions, and do not always reflect what the songwriter/singer may have written/recorded (I have seen some pretty serious howlers when finding songs for my own playlist). And the thick brogue and toothless enunciation of Shane McGowan is particularly difficult for those not familiar with Irish speakers. Finally, the similarity of the irish pronunciation of tree and three are well attested in humour - which I indicated by my use of the 
[FOGHORN LEGHORN]That’s a joke, I say, that’s a joke, son[/FOGHORN LEGHORN]
Welcome to the dope, we do hope you’ll enjoy your stay, but spend a bit of time lurking until you get a better feel of how we work, and your interactions will be much more enjoyable and productive.
Your condescension is endearing. Great way to make sure I “spend a bit of time lurking”. What is this, 1996? Because I haven’t used this username on straightdope before, I have no idea how a message board works? Seems more like a way to indirectly detract from the actual content of my post.
Being Irish, I’m familiar with pronunciation quirks that are “well attested in humor.” But sticking with my original assertion, those jokes are all based on “threes” being substituted with “trees,” and never vice-versa.
I’m looking at the lyrics of the song as they’re printed on the inside dust jacket of a copy of the album. It says “coming up three boys” not “coming up threes” which leads me to believe that it is probably referencing the dice game Hazard mentioned above.