Don't change Lapras for Gyarados.
As for your sixth spot, maybe get Gallade or Medicham, since you want a fighting type. If you get Gallade, use this moveset. Close Combat, Psycho Cut, Leaf Blade, and Rock Climb if nobody else in your party has it. Swords Dance if somebody else already has Rock Climb.
As for levels, around 80 is best, 70 is the minimum reccomended, but 60+ is entirely possible if you can use items effectively. It will take paitence, but I have beaten Red, so you can too.