I am not familiar with Lutheran General.
I do have 3 grown children. The first was born while I was under the effects of an epidural. The other 2 were born without the use of any pain medication.
Of course it hurt but I could FEEL the birth of my child. With the epidural, I lost all feeling in my pelvic area. It was difficult to push because I couldn't feel.
Personally, I think you should avoid the use of all drugs and don't let them give you an episiotomy. You will tear naturally and the tear will heal faster than the artificial cut of the perineum.
My first child was born with an episiotomy being performed on me. Of course I didn't feel it because I had an epidural going.
The other two were born without the episiotomy. In both cases I tore but I didn't feel the tear because it happened in the midst of the birth.
I had trouble with the episiotomy regarding pain and healing. There were no difficulties with the natural tear in terms of healing. Was I sore afterwards. Yes of course I was but after soaking in a tub with the herb Uva Ursi I just healed up.
FYI. My first child was born in a hospital environment when I was a teenager.
My second child was born at home.
My third child was born in a hospital.
I mention the above facts because you can get what you want if you and your partner know what you want in terms of your birthing experience. You and your partner must be real advocates for you and for your child. This is your birth experience, not anyone elses, and it should be what you want it to be, to the extent that is possible in the hospital environment.
One thing I would add is that the drugs can have an adverse reaction on the sensitive newborn system and can create a situation where mother-child bonding is interrupted because the child and mother are suffering the after effects of medication.
Peace and best wishes to you and your family.