I gave follower Lydia a steel great sword of arching and watched her fry people with it, but it doesn't discharge. Is this typical of followers with enchanted weapons or a bug?

Sounds like a bug... I haven't used followers yet as they constantly get me discovered while sneaking but I see no reason why it shouldn't discharge as it would if you used it yourself... However it could be out of charges but I think you'd have probably checked that...

Well since they have unlimited arrows it's possible for them to have unlimited charges too. Will have to test this since I've yet had the need to put an enchanted weapon on my follower.

I noticed that NPCs dont use up enchanted weapons.....i guess that because of how annoying it would be if you have to keep recharging their weapon for them.

They uses charges and arrows, however much slower than you.
Are you sure she uses the correct sword, they have odd choices in equipment, tend to prefer unimproved and unenchanted gear over legendary double enchanted of same or better materials.

it's likely that they go through charges similar to how we do eg based of destruction skill for damg enchants with a npc modifier instead of pc modifier while it's imposible to make her skill up destruction. it's very easy to see if they used up charges just trade them items with charges and see.

My Lydia uses charges and arrows. The charges do seem slow to expire, but I know she emptied the dwarven axe of absorbing when I stopped seeing the HP siphon effect. Seems everyone's game is different. I haven't seen her run out of arrows, but I do refill her stash evey now and them.

Supposedly, the higher your skill, the less charge is used each time. Maybe Lydia has a decent 2-handed skill, allowing her to use the weapon without depleting the charges too quickly.

I have a hard time believing this is actually the case though, since I have 98 archery and my Nightengale bow depletes fairly quickly- in maybe 20-25 shots? I thought it would last a lot longer.

Yes, it's the only weapon she has besides a bow and I've checked the charge several times and it hasn't moved since giving it to her. I also gave her some iron arrows and they do decrease and I find them in creatures she's shot.

Cheap. I give her Orcish arrows.

As you said, they get used and I find them in her targets.

Someone mentioned an aversion to enchanted weapons. I see something similar with an Orcish Greatsword as opposed to a Steel Battleaxe; she's using the steel even though the orcish is a lighter weapon of the same damage. Maybe they gave her an axe perk?

My companions don't use up arrows, I know this for a fact because I always give my companion one of whatever my highest quality arrow is and I use them to duplicate more of it by picking up the arrows that miss. I did notice Lydia used up a staff of lightning she picked up from god knows where (I didn't give it to her, one day I was fighting a dragon and she just HAD IT suddenly, I just let her keep it).

I've been running with Vorstag for a few days, and I've noticed that he doesn't seem to use charges in his enchanted weapons, either. If he does, it's really really slow. You can see what they have equiped from their inventory window the same way you can tell what you have equiped.