That is a hopelessly naive description of lobbying, to the point that I assume you are being intentionally disingenuous. Lobbyists commonly funnel money to politicians via fundraiser bundling, donations to outside spenders like PACs, and other mechanisms that get around the weak remaining restrictions on direct campaign contributions that SCOTUS has not yet gutted. A lobbyist may not donate directly to a politician's campaign, but they get a group of their friends together for a fundraiser to effectively donate on their behalf (bundling). Or they donate to outside groups who then spend to support the politician's campaign, e.g. by funding advertising that benefits the candidate or hurts their opponent. Like when AIPAC sinks millions into ads against progressive candidates, that's tightly connected to their lobbying on behalf of Israel and you better believe that the politicians benefiting from that spending are well aware of how it is connected to their willingness to adopt the lobbyists' positions.