Tra la la...away we go...

After I had tidied the arena and put my gear away, I trudged deep into the bowels of the manor to the girl’s holding cell. Apart from her, the cells were empty. The two wardens stood outside and unlocked the door for me. Myself and the girl didn’t have any privacy as the wardens listened through the bars.
"Myself and the girl..." is ungainly as hell.

Part of my job was to explain the execution procedure to the girl.
I sat on the chair opposite her and I explained in minute detail every aspect of the hanging. She listened, again impassive. After I had finished my explanation I leaned across and clasped her hands in mine. Gazing into her enchanting eyes I told her everything I wanted to say.
Try "Explaining".

“You took your flogging well. You didn’t show them any pain. I’ve got to give you that.” She smiled weakly. “Look, you need to be strong tomorrow. You show them any weakness, they’ll love it.”
“Aren’t you one of them?” She had me there. I paused, trying to think of something to say but I couldn’t.
“Yes. But I didn’t want it to happen this way.” I noticed her eyes were looking at my neck.
“Isn’t that a Saint Christopher’s medal?” I looked down at the pendant around my neck.
“It is. Patron saint of travellers.”
“I was wondering if maybe you could let me have it. I’m don’t want to be alone on my journey.”
“Lana I’m sorry but it’s kind of a family heirloom. My mother would kill me if she knew I gave it away.” She looked disappointed. “Remember what I said, be strong, be brave. Whatever about the rest of them, I’m rooting for you.”
This was fine but would have been better served with a brief touch on the main character's departure. This could have been quite a sad moment - an exchange between the two as one left the room.

My husband never asked about what I did at work. In fact he grew tired of the stonewalling whenever he asked. I just told him that I worked for the government and I was bound by the Official Secrets Act and if I told him anything, I could go to prison. In reality, if I told him anything, I’d be hanged.
How about "had I revealed the truth"?
Try to find different ways to phrase.

I can recall (as bad as my memory is) an author who would ocassionally wind up a punishment but deliver it as a reward. In essence, your last sentence here would have been put "the reality was that, had I revealed the truth, my reward would have been a proper hanging from a stout tree." Little things like that can add to the starkness of situation, I've noticed.

I lay awake on the pillow beside him while he sat up in bed reading Bukowski. As soon as his eyelids began to droop, he put (putting) the book down and noticed (noticing)I was still awake. He kissed (kissing) me on the lips and noticed (noticing) my sullen demeanour.
Get away from so much passive writing. everything is past tense here. As stylistic as you tend to be you forget to stylize your action...even if it's not terribly active. Clearly, you can't make eveyrthing active...the parts in red there are to illustrate where you could get rid of some of the passive phrasing and bring things a little more immediacy. Just change one of the passive words in each sentence and you can change how the paragraph reads. Remember, you have to vary how things are presented and things are almost always presented in the past tense with this story.

“Anything wrong?” I faked a smile.
“No.”
"Anything wrong?"
"No," I said, faking a smile.

“OK then, good night baby.” As he snored, I still lay awake thinking of the girl. I felt lousy for not giving her my medal. Maybe there was still time to make it up to her. My conscience had never felt this bad about an execution. The ones I had previously hanged had killed their masters. Maybe I didn’t think hanging them was right, but it was better them than Lana. Gradually, with a heavy conscience, I drifted off to sleep.

I waited patiently on the gallows for the wardens to bring the prisoner out. Again, the mask obscured a small part of my face. The clank of chains and the thump of feet on wood became audible and Lana appeared up the steps, bound like she had been the previous day and wearing the organisation’s uniform, just as I wore. They led her over to the trapdoor and unbound her. Then, they retired to the room beneath. Myself and Lana were completely alone.
Nothing in her face revealed the abject terror she must have been feeling. I respected her for that. That young girl standing tall atop the gallows could so easily have been me ten years ago. I shuddered at the thought. It was time for me to get to work.
“Have you anything to say before sentence is carried out?” She was silent. I tied up her hair pulled the black hood over her head. Lana would never see the light of day again. It was such a waste. I strapped her long, slender legs together at the ankles and cuffed her hands behind her back. With a short length of rope, I pulled her elbows together and bound them, hoisting her young breasts upwards. As a final dignified act, I wrapped wound some rope around her skirt so as it wouldn’t flap when she went through the trapdoor. Believe me, there were people down there looking up.
I dropped the noose dangling from the beam above, over the hood and tightened it around her beautiful neck. With that, Lana was ready. I went to the trapdoor lever. The drop would take place at my discretion. Looking at her, I thought of one last thing. Unclasping my St. Christopher’s medal from around my neck, I walked over to her and pressed it into her hand. She must have known what I was doing, as she grasped it in her palm and squeezed.
A lump formed in my throat as I tried to delay the drop for as long as I could. Eventually, I decided I must proceed. With a heave, I pulled the lever back. Lana fell and after travelling quite a distance the rope snagged and I heard a crack. It swayed and rocked from side to side. With every execution I had done, there had been a cheer from the crowd below, but now there was silence; just the creaking of wood as a tear fell from my mask. I marched quickly away from the gallows and back to my office
I sincerely hoped that I had done my best for her- that she hadn’t felt any pain. They’d be taking her down now for burial or cremation. I typed furiously on my keyboard and produced a short letter. Barging into Lydia’s office, I didn’t knock. I slapped the letter on her desk.
“What’s this?”
“Read it.” Lydia opened the envelope and scanned through the letter, stony faced.
“So you’re leaving us?”
“In two weeks.”
“What made you decide?”
“I couldn’t do it any more. Seeing that girl dangle at the end of that rope made me sick. I could see myself in her.”
“Of course, you never went down the slave route. By the way, don’t you owe us a debt?”
“As far as I’m concerned, today, I paid it.”
The next two weeks drifted slowly by. Some of the girls in the administration end bought me a cake. The whole thing was nothing out of the ordinary- just like leaving any office job.
As I pulled away from the manor in my car for the last time, I looked in my rear view mirror and saw Lydia leaning against one of the Doric columns looking out nonchalantly over the estate. I don’t know whether she knew it or not, but beside her stood Lana, smiling and waving. I smiled back.
Okay, I am not going to bounce you on each and every passive moment or each poorly phrased sentence. You got the drift, I am sure.

Question: Did your character sound like a woman? Did she talk like a woman? I didn't get that at all. She sounded like a man. Remember, women tend to find things that men tend to ignore. They also tend to ignore things men tend to see.

Assignments:
Work on finding your female voice.
Work out your tendency towards the passive voice.
Work out your tendency towards wordiness (be economical)

Now, go get me a re-write of this story so I can rip you another new one. I figure that, by the time we are done with this story you will have 5 or 6 new assholes. Sounds harsh but you will never be constipated again!

Dean