swecology,
I haven't built the Lyman kit but I will pass on my experiences with the CVA Hawken kit in that I think they may pertain to what you will find.
I got my kit for $50 from a friend who had purchased the kit, found all the brass parts were raw sand castings and tried to polish out a few of them. After spending quite a few days and still being nowhere near the way he wanted them, he stored the kit in a closet and left it there for 15 years.
He rediscovered the kit while doing spring housecleaning and decided he still couldn't polish out the brass parts satisfactorily and so came over, put the kit on my patio table and said "50 bucks and it's yours. I can't polish the brass in this lifetime."
The finished rifle now hangs over my fireplace along with a Philadelphia Derringer kit he also couldn't finish.
I had no trouble polishing out the brass in this lifetime because I have a buffer and a lot of sticks of rouge for polishing. And it still took a month or so of weekends to do it.
The moral of the story is that if the Lyman kit has raw sand castings for the brass parts and you want a high shine, get a buffer or spend a LOT of time doing it by hand.
Ka6otm