Sniper 99/70
+99 luk base stats
+8 luk job bonus
+99 agi (relevant)
Skills
True sight (+5 luk)
Upper headgear
(+6 luk) +9 Tiraya with Dolomedes card
Mid headgear
(+4 luk) Nobel gem
Lower headgear
(+2 luk) Orichalcum backpack
Note: +5 luk instead on heRO 10th birthday
Armor
(+10 luk) Black wing suit with Venatu card
Garment
(+8 luk) +10 Black wing manteau with Green Maiden card
Shoes
(+5 luk) Crystal pumps
Accessory
(+10 luk) Brisingamen
Accessory
(+10 luk) Brisingamen
Weapon
(+5 luk) Fortune sword
Shield
(+2 luk) Any shield[1] with Zealotus card
Extra headgear for switching
(+30 luk rng for 10 secs when damaged) headgear[1] with grand peco card
Food +10 luk
Pet Lunatic with silk ribbon
(+3 luk for 10 seconds every 50 seconds)
Total: 217 luk
or 220 if you count that note on orichalcum backpack.
Note: I think I also found a set that's better than this, but I'll post later when I'm not lazy.
Edit: Forgot shield
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Edit 2: New answer
I was going to post about a Blacksmith set that can clutch 1 more Luk than the Sniper set I wrote but then I figured something out about assassins.
Assassin 99/70
+99 luk base stats
+8 luk job bonus
+99 agi (relevant)
Upper headgear
(+6 luk) +9 Tiraya with Dolomedes card
Mid headgear
(+4 luk) Nobel gem
Lower headgear
(+2 luk) Orichalcum backpack
Note: +5 luk instead on heRO 10th birthday
Armor
(+8 luk) Any armor with +3 luk enchant with Venatu card
Garment
(+5 luk) Any +10 garment with Green Maiden card
Shoes
(+5 luk) Crystal pumps
Accessory
(+10 luk) Brisingamen
Accessory
(+10 luk) Brisingamen
Weapon
(+10 luk) Excalibur
Shield
(+10 luk) Excalibur
Extra headgear for switching
(+30 luk rng for 10 secs when damaged) headgear[1] with grand peco card
Food +10 luk
Pet Lunatic with silk ribbon
(+3 luk for 10 seconds every 50 seconds)
Total: 220 luk
or 223 if you count that note on orichalcum backpack.