The key is who you're lobbying. If you're in a hard right or hard left district with a rep that is inflexible your lobbying will be ineffective. But every vote has a handful of politicians that have no strong opinions or ideological grounds on that vote and are movable. With proper organizing one can target those districts and call citizens of those districts to then call their representative.

But as citizens who haven't organized, if everyone contacts their representative at least some of those communications will be with the politicians that can be moved.

I've done the former and the latter and been part of bills getting passed that otherwise probably wouldn't have. Cynicism is the strongest barrier to progress. It doesn't mean it will work every time, but it absolutely works.