That definition of lobbying might have worked a few centuries ago. But nowadays it means trying to influence someone's opinion and throwing pre-written policies (and oftentimes money) at them.

Also, the definition of corruption you seem to have is not accurate IMO. Corruption is what Spiro Agnew did: trade explicit influence in exchange for some dosh in an envelope. That's not what politicians usually do today in western democracies -- which is to say, pay very close attention to what their major donors are worried about. There's a case to be made about how the two are equivalent in the end, but the fact of the matter is that in the first case the funds arrive in an envelope for the politician to pocket (minus some bagman commission) whereas in the second case the donations are (supposed to be) disclosed and (theoretically) benefit the politician's campaign.

It's not just campaign contributions though. When people step out of government they're often stepping into very cushy and lucrative jobs provided by people they helped while in government. You don't get to make that transition if your primary motive is looking out for the average citizen. It never even has to be agreed to explicitly, it's just understood by all parties how the system works. Very hard to prove corruption in that case, as it's institutional rather than individual.

Speaking personally, I'd rate that as a career choice/part of the job thing. It's like, if you've little to no interest in working for this or that large business, you've no reason to pull any punches against them - but it's a career choice at the end of the day.

Also, keep in mind that when a congressman leaves office, they usually have relationships with people that can move the needle in government. As such they can do valuable things for whoever is willing to hire them -- regardless of the positions they held while in office.