Oh the wonderful world of pain management. >.<
I remember being stoic when I had mine done pre-HRT. No drugs, I just shut my eyes and focused on slow deep breathing. I found that worked well as most of the discomfort was felt on initial insertion - it turned into a minor buzz after about a minute. I was having 3 hours sessions on a 16 probe galvanic for reference.
Having been on HRT for 2 years, I have to say that the discomfort I felt the last time I had a touch up was more marked, but I found slow regulated deep breathing still worked well.
My ideas/suggestion for pain management, going up in level of intervention:
1. Deep breathing and meditation. Pain is very much a personal perception - if you go in with the attitude, this is going to be agonising, it will be. A positive attitude "there will be minor discomfort" will move the goal posts - pain is a very emotive word and best avoided.
2. Ice - an area that is iced will have lower pain perception. Note that this will constrict the follicles and make it harder for the electrologist to insert the probes.
3. Pre-meds - non-steroidal anti-inflammatories are your best bet. Don't exceed dosages - past a certain dose, most over the counter analgesics have no additional pain mediation effect.
4. EMLA cream - apply liberally over the area and cover up with something for at least 1 hour so it doesn't dry out. Expose an area as it is being worked on. It has limited effect as skin is a very effective barrier.
5. Dental injection - a full cartridge injection of lignocaine with adrenaline or prilocaine with octapressin will give 2-3 hours of anaethesia. If you're lucky and your dentist does a lot of surgery, they may have bupivicaine which will last a lot longer.
The other important thing is to make sure your technician is always doing some work on the upper lip every session mixed in with other areas at the same time. If it's spread out amongst the other areas being managed, it is much more tolerable. In a multi-electrologist centre, they all tend to skive off the upper lip, hoping that the next person has to work there.

I hope that helps.