How to make my follower to wear same type of armor as her default, but improved?

Long story short: my loyal follower Lydia is now a Blade. Upon taking her oath, she got full set of Blades armor and it became her default armor meaning it's not seen in her inventory - not even when pickpocketing her.

I also got my own full set of Blades armor and being good hearted thane decided to improve it and give to Lydia so she will have better chance surviving the oncoming battles. I improved it all to Epic and gave to her, however she just won't wear it, staying with her default and plain set.

1. The armor rating is much better in every piece of armor.
2. If I give her different type of armor with better rate she wear it on spot.

So, while it's quite obvious what's causing this issue I have no idea how to "fix" it other than killing her, taking the plain set from her body then revive her with console. So far I managed without console and really hope to keep my hands clean.

I went over all answers in this related question and the one suggesting using a mod sounds promising, but prefer to hear someone confirming this mod before installing it.

Any ideas? Maybe there is a way to make her resign from the Blades?

The mod you linked to, TCG - Tradable Companion Gear can indeed allow you to remove all of your follower's equipment, even those that are considered part of your follower's "default gear" (doesn't appear in the follower's inventory, and is unremovable in the vanilla game) - the Blades armor, in this case.

TCG is now also part of a bigger follower ovehaul mod, UFO - Ultimate Follower Overhaul. They are made by the same author.

TCG description from its webpage:

• All followers gear can be traded.
• Default hidden bow and arrows are tradable and not respawnable.
• Followers will not revert to default outfits or unequip gear even if dismissed.
• Followers will wear what is placed in their inventory.

With TCG or UFO, just open up the item inventory screen of Lydia and remove her default Blades armor, and then put in the improved Blades armor that you have.

IF you are playing on the PC, the following steps should work:

• Open the console
• Click on her face
• Type removeallitems and press Enter

You can not see her armor because she has it equipped. This prevents you from stealing it via pick pocketing unless you have the perk that allows you to do just that, take what is equipped.

When having the same suit of armor but you have improved it either through smithing or enchanting the gear, the only way that the NPC will equip it is if it was their gear to begin with. This means you have to steal what they are wearing, boost its abilities in any way you see if and then return it to them before the magical tick time that will respawn their gear.

If you do a bit of browsing on some fan sites (I recommend the Unofficial Elder Scrolls Project's Wiki) you can even find a list of NPCs and how many pieces of 'natural' gear they have that you can then take and improve for them. Maybe someone will be kind enough to edit that URL in here for the both of us.

Hope this helps.