since you have to cache price_type on every table, you could use callbacks to not have to do this in a... controller action? or wherever. This could be a first step to simplifying. 
class Quiz < ApplicationRecord
  belongs_to :lesson_plan
  before_save :set_price_type
  def set_price_type
    price_type = lesson_plan.price_type
  end
end
class Document < ApplicationRecord
  belongs_to :lesson_plan
  before_create :set_price_type
  before_save :set_price_type
  def set_price_type
    price_type = lesson_plan.price_type
  end
end
class LessonPlan < ApplicationRecord
  belongs_to :private_class
  has_many :documents
  has_many :quizzes
  before_save :set_price_type
  after_save :update_relationships
  def set_price_type
    price_type = private_class.price_type
  end
  def update_relationships
    quizzes.update_all(:price_type, price_type)
    document.update_all(:price_type, price_type)
  end
end
class PrivateClass < ApplicationRecord
  belongs_to :private_school
  has_many :lesson_plans
  after_save :update_relationships
  before_save :set_price_type
  def set_price_type
    price_type = private_school.price_type
  end
  def update_relationships
    lesson_plans.update_all(:price_type, price_type)
    document.update_all(:price_type, price_type)
  end
end
class PrivateSchool < ApplicationRecord
  has_many :private_classes
  after_save :update_private_classes
  def update_private_classes
    private_classes.update_all(:price_type, price_type)
  end
end
then you don't have to do anything extra to keep price type up to date.
The much larger and tougher question to answer is why is this variable being cached on each table in the first place? This is going to eventually make maintenance a nightmare. You need to take a hard look at where you are accessing this value and ask yourself if you really need to cache it.  
These decisions are made usually in response to slow queries in views or controller actions, but most of the time that slowness can be resolved in better ways.  In general, favor query optimization over denormalization