If Lydia equips a pair of boots that are enchanted to give a +40 carry weight, does she receive the bonus?
TL;DR: The answer is yes.
I could have had this tested within 10 minutes, were I not quite so particular in regards to the parameters of my test. The particularities cost me several fast travels, and a dragon encounter in Riften (my adopted home town - I could hardly ignore that). But, test this I did. In the end, it was an interesting 45 minutes.
And before any of you say I could have done something differently with the console, please remember I'm on a PS3.
This test could have been done with any follower. I had two in my Riften home: Iona, my housecarl, and Jordis, my wife. However, you specified Lydia in your question so I decided to go to Whiterun and get her.
To keep this test as clean as possible, I wanted to start us both with our inventories as empty as possible. This meant dropping everything I had, clothes included, into a chest at home.
The next step was trying to relieve Lydia of the same. Strangely, despite my level 100 Pickpocketing, this was a more difficult task than I had anticipated. The first time, she caught on to what I was doing, and darted out the nearest door to fast-travel back to Whiterun. When I got to Whiterun, I saw that she'd somehow procured her armor again and so I'd have to start over.
I took her back to my Riften home again, and this time started in the basement so that I'd have a chance to catch her before she got out the door if she chose to run. Still, she swatted away at my advances. Now I knew we needed some quality time outside for her to cool down before I could try again. So, I decided we'd take a walk about the Riften stables. That's when the dragon showed up.
I quickly ran into Riften, hoping he'd be content to stay outside. However, he was having none of that. He followed Lydia and I into the city, where he continued his rampage. Without my enchanted armor, I knew I didn't have enough power to defeat him head-on. Also, with Lydia only partially dressed, I didn't expect her to fare well in the fight either. So I dashed into my house, threw on my best Dragonscale Armor, and came out ready to fight.
The guards were already hard at work, but making little progress. Lydia was doing what she could from a distance, with that odd bow and arrow set that I can never seem to take away from her. (Sure, I can manage to pick off her armor, boots, gauntlets, and shield - but somehow the bow and arrows are off-limits.) I went in, hands aflame, and made short work of the beast myself.
After all was peaceful again, we went back inside and I dumped my inventory into the chest again. This time, perhaps not having much energy left to fight, Lydia seemed a bit more cooperative with my efforts to empty her inventory as well. I dropped all of her stuff into another chest, then retrieved her boots and one filled Grand Soul Gem I had in a cupboard.
Lydia looked on as I took these to the Enchanter, and loaded up the boots with a +37 Fortify Carry Weight. Then, we went to the master bedroom where I had my potions stored. As we came up the stairs, I saw my wife Jordis turn and walk away in disgust. Our housecarl, Iona, simply rolled her eyes and continued drinking her mead.
I threw Lydia's boots on the bed, so that I myself would start with zero effective weight on-hand. I'd chosen potions because they are small and uniform in weight, allowing for fairly accurate and granular measurement. Plus, I had an end table packed to the brim with naught but a crap-tonne (that's a metric crap-ton) of them.
In a flash, I had myself over-encumbered with 699 weight units of potions - a total of 1,398 little vials. I knew I'd hardly need all of these, but I figured it was the easiest way to start. I began with the largest batches first, and gave Lydia as much as she could carry:
I still had over 500 weight units of potions in my stock, but now I could move around a bit. Looking at Lydia's boots, I saw that they weighed 8 units. So, I took 16 of the Restore Health potions from her (at 0.5 units apiece) and handed her the boots. After she put the boots on, I chose a different potion to measure how much (if any) her carry capacity had increased. She was able to take a total of 74 Regenerate Health (+150% for 5 mins.) potions before becoming overloaded. That's 37 additional weight units, which was the exact amount of the bonus provided by the boots. She now had a total effective carry capacity of 232 units.
Of course, I couldn't let her go wandering across all of Skyrim in the buff as she was. So, once we were done with our little chemistry experiment, I graciously relived her of the potions and returned her equipment. I even allowed her to keep the newly-enchanted boots.
Iona let out a sigh of relief, while Jordis stormed off to bed. I suppose I'll have to get my rest in Whiterun tonight.