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! A devastating bow (of ancient Spartans before 700 BC) 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. And saving your arrows when you hit very hard targets.

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.
Just like a young Spartan of those times.

The easy way - you can steal it in Whiterun's Hall of the dead. Placed one there for testing.

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

UPDATE.
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. 
Perfect for the bow. Actually not just the Spartan bow, but all the bows you use
in game will get this improvement. So if you already have a great bow you like,
you can benefit from the optimal 4x zoom. Which is perfect for both mid- and long range
battles, if you are a skilled archer.
What if you hold your trusty bow and a bandit or a wolf suddenly jumps at you? The last resort that can often
save you in close battle is Bow Bash created specifically for such cases.

UPDATE 1.1.
Corrected some font errors.

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

Choose and install one version. Not both.