Improving the Lightning bow I've come to 2 conclusions.

1. It should be very simple-looking, lore-friendly, easily upgradable and enchantable.
2. The critical damage should remain and be slightly modified.

Here it is! The bow with the damage power of a Daedric bow, very fast as the Zephyr bow,
upgradable with 2 steel ingots. Can be enchanted. The critical damage is still very high,
and it should kick in every 5 shots, randomly. Which makes your shooting unpredictable and
intense.

You can craft it at a blacksmith forge using 1 steel ingot, 1 iron ingot, 1 leather stripe
and 1 bear claw. Which means you have to kill a bear somehow before crafting it.
(3 bears live in Honeystrand cave, it is to the east of Riverwood, south of Ivarstead).

The easy way - you can steal it in Whiterun's Hall of the Dead, if you play on Legendary,
hunt and defeat one bear with it if you can, than go home and craft your own. Drop the stolen one into the river.


Installation.
Download, unpack and put it in your Data folder or use a mod manager.

UPDATE.
Just made a version which enhances the zoom in the Eagle eye perk by around 25 percent.
Tried the most popular bow zoom mods, too much for me. The zoom is too enhanced.
Some testing shows the optimal. It is plus 25 percent to the Eagle Eye perk.
Actually not just the Spartan bow, but all the bows you use in game will get this improvement.
Practically it's x4. Which is optimal for bows to clear 3-5 very distant targets in a minute, in Skyrim.
And then charge closer hitting 2 more, and putting out your elven dagger when it's close fight, Imho.

Testing shows that if you already have the perk, it enhances also.

Choose and install one version. Not both.
Recommended to use it with faster arrows from Fast life.

UPDATE 2.
Now I installed the English-language Skyrim, so no more garbled symbols.
The Spartan zoom descriptions ingame are fully in English, and the archery level when
you can get the Eagle Eye Enhanced perk is moved from 30 to 20. 
Which makes it easier to get and try ingame.