Yes, Lucian Jungle does work. Your first clear is horrid, but as you get into mid game, farming becomes a breeze, and you become a carry for your team. Lucian jungle is super fun to play, and with all the CDR in this build, you will see why I love to play Lucian in the Jungle.

The Warrior enchantment on Lucian is godly. It gives you 40 AD, 10% CDR, 10 Armour Pen, and additional buffs to monsters. Personally I recommend Trailblazer as it helps you sustain and clear your jungle more efficiently, but Chilling Smite and Challenging Smite are both good alternatives.

Ionian Boots are amazing on Lucian. After having just your Warrior enchant and Ionian boots, you have 25% CDR. This will allow you to E much more often. Make sure you use Lucian's double shot passive, in order to further increase the cooldown on your E. You become a kiting god once you get Ionian boots.

The rest of the build is pretty self explanatory.

BOtRK gives you Attack Speed, Life Steal, and Damage, as well as a % health passive and the active. This makes it much easier to clear camps, as you will be able to sustain for much longer.

Shiv and IE both give you crit, making your attacks just do tons of damage.

Bloodthirster is amazing lategame, as it gives you a gigantic shield, and Lucian scales considerably well with lifesteal.