Nothing stops citizens from organizing a non-profit to lobby the government. I’ve worked with a few groups that lobby for better healthcare coverage. They go to Washington once to year. They are surprisingly effective in getting changes passed.
Actually being more “grassroots” makes the lobbying easier. It’s harder for a Congressperson to reject a meeting from their constituents.
American People Hire High-Powered Lobbyist To Push Interests In Congress
"WASHINGTON—Citing a desire to gain influence in Washington, the American people confirmed Friday that they have hired high-powered D.C. lobbyist Jack Weldon of the firm Patton Boggs to help advance their agenda in Congress.
Known among Beltway insiders for his ability to sway public policy on behalf of massive corporations such as Johnson & Johnson, Monsanto, and AT&T, Weldon, 53, is expected to use his vast network of political connections to give his new client a voice in the legislative process."
https://politics.theonion.com/american-people-hire-high-powe...
"In it's grand equality the law forbids both the rich and the poor alike from sleeping under bridges"
I mean, sure the lobbying system is "open" to all, but not everyone can actually participate in it or utilize it, even if they're technically allowed to.
Here is an example of a state bleeding disorders non-profit that meet with Senators in DC every year.
https://cthemophilia.org/events/washington-days-2020/
I also worked with an entrepreneurship group at a college. The head told a story where he went to DC and his senator had their staff type up the law with him there. Brought it to the floor that day. It didn’t pass but I was amazed at what got done through one person’s advocacy.