Snowboarder here. I just took my gf out to a bunny hill to learn how to snowboard.
FIRST AND FOREMOST - GET HER PADDED SHORTS.
The snow really sucks so far this season. Whether the snow is natural or not, unless you're going to Wolf Creek or somewhere in New Mexico.... she will be learning on hardpack.
The entire first day of snowboarding is falling down. I gave my gf my impact shorts (which didn't really fit, but still protected the key areas and she was very thankful for how much it protected her. (I, on the other hand slid on some ice and hurt my tailbone).
Second - A lesson is a *good* idea. Even if both of you are patient, you will both enjoy her first day of riding much more if she is being taught by someone else. You can go do a couple of laps while she's in the lesson. You guys can meet back up after the lesson and then you can spend the rest of the day waiting on her and being helpful as she inches her way down the hill, falling all the way (there will be no shortage this, trust me).
I am a big fan of first lessons AFTER the newbie has figure out how to strap in, walk around and stand themselves back up... but some people can barely manage that even after their first half day.