What is the best 1.9 magic fishing rod for catching treasure?

Since 1.9 made afk fishing a very easy and profitable endeavour (because you can use magic mending/unbreaking rods and ditch the rod storage/dispenser mechanism) and on top of mending you can use luck of the sea / lure and mending+unbreaking.

I have been using the following rod to afk fish:

Unbreaking III
Luck of The Sea III
Lure III
Mending

But I came across this reddit post, with a very detailed analysis:

Based on this I calculate the average time (seconds, rounded to nearest integer) between treasures for each Lure/Luck combination:

Lure↓\Luck→     0       1       2       3
          0     500     417     357     313
          1     500     400     333     286
          2     583     438     350     292
          3     750     500     375     300

As you can see, Lure 1 and Luck of the Sea 3 is the best combination for time efficient treasure finding.

There were several changes to fishing in 1.9. What is the best magic fishing rod for catching treasure?

You are using the right fishing rod. There is one change in 1.9 that made the reddit post obsolete:

Minecraft 1.9 Changelog:

15w43c Lure no longer affects loot.

It means that the reduction of 1% per level on treasure is no longer in effect. So the faster you fish, the more treasure you get.

The best fishing rod for catching treasure then has

Luck of the Sea III
Lure III

Adding mending and unbreaking while a good choice to save experience points, are irrelevant to the chances of treasure.

On a world without plugins or commands I AFK fished for 2 hours using this fishing rod:

• Mending I
• Lure III
• Luck of the Sea III
• Unbreaking III

I used all the books I got and I got my Diamond Armor all Protection IV, I got my bow to Power 5, Infinity, Mending, Flame, And Punch 2, My Pickaxe became eff. 5 fortune 3 Mending and Unbreaking 3.

I recommend this strategy for AFK fishing if you want to get good gear if you have the patience.