I've found this bug is very common while I looked for how to fix this.

When I enter Calelmo's lab the wizard's guards are hostile although I got the key peacefully by killing Nimhe for Calcelmo.

Upon seeing me, the Markarth guard adds 5 bounty on me and asks me to pay for it. I pay, get teleported, then get back, and the same exact thing happens.

While in Calcelmo's lab, my follower (Lydia) tells me "You're not supposed to be in here!"

This is frustrating me, please try and help...

Thanks

sorry its not a bug

the key only gives you free access to the museum ONLY and that's it..........beyond that point your trespassing ..........that's why Lydia is grumpy ...................also you have to do some other quests before you go into the lab

So how am I supposed to get beyond that Markarth guard without killing him (because killing him would make all of the city hostile (I think...?)).

And what quests I should complete before going into the lab?

Thanks.