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.
- The armor rating is much better in every piece of armor.
- 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?