You rightly mention lobbying and corruption together. But somehow you miss that they are on the same continuum. From my EU perspective lobbying in the US is corruption, as the lobbying comes with money and paid-for political promotion.
The situation around guns itself is a clear example: as I understand it, a majority of US people is in favor of more limitations to gun rights (banning automatic weapons, screening psychiatric patients and criminals) but politicians are only expanding gun rights (open carry etc).
If democracy would work as intended then "common sense" limitations would have been introduced long ago.
Note that I am not talking about corruption in the criminal sense: US politics and supreme court have fully legalized and embraced it, conflating it with lobbying.