Is it possible that a distinct lower-class culture exists?

Yes

Explanation: Lower class culture is defined as a set of behavioral expectations imposed on a specific group that eventually become a barrier to their success.

For example, many parents in low-income neighborhoods discourage their children from pursuing higher education because they believe their children will be unable to compete with children from middle- to upper-income families.

the catholic church withhold people's access to the bible during the middle ages.

people could go to church and listen to the teachings, but it was absolutely forbidden to own and/or read the books of both the old and new testaments. it was also prohibited to translate the books (which where originally in biblical hebrew) to any other language.

this was done so the church could remain in control of what their teachings were and to enhance their importance and power, while also being able to judge people's actions through information that was unavailable for the general public.