The Elder Scrolls V: Skyrim – Can Mehrunes Razor Accidentally Kill a Follower?

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.

There are chances where the follower is stuck in a position, could be this or also in fighting stance.

Normally the best way is to load a saved game before this happened instead of continuing to play since there is a chance that this is not possible to fix.

Other options would be to do something that resets the position. I would try to use the fus-roh-dah on her to throw her over. She will then have to get up again form the floor.

The change of stance needs a trigger. So to sheath the weapons or to get up from crawling, there needs to be a change in situation that causes the trigger. If the system overlooks one trigger, the follower is stuck in the stance. You have to re-initiate a trigger to change the stance again. I am not sure what kind of attack would work since I am not sure how the follower would normally react to an attack while crawling. However a fus-ro-dah normally topples players over completely and then initiates the "get up from the ground" movement, and I am quite sure that if you manage to topple her over, she will not get into the crawling stance.