You are absolutely right about lawmaking being a profession, but in a lottery system, I reckon these professional lawmakers would simply be hired by the representatives, and they could stay on for as long as they are deemed useful. The representatives would act more like full-time overseers on the executive and legislative branches, if that makes sense.
Junior lawmakers are also perfectly capable of hiring senior lawmakers yet the balance of power still shifts towards lobbyists, so I would assume that the same issue would exist for lottery-drawn representatives.
Perhaps. I think there are generally three ways lobbyists can exert influence:
1. By nurturing personal relationships with politicians. I may be mistaken, but I feel like this is probably the most effective method. You want to exploit the natural tendency people have to want to help their friends, even decent people.
2. By helping politicians get what they want (e.g. reelection, but also first election, or election to a new position).
3. By providing compelling arguments and objections to various policies, grounded in special knowledge about their industry. These compelling arguments may be good (in which case the lobbyist's influence is actually a good thing), but they may also be bad (misdirection or lies).
I think lottery is less vulnerable to 1 and 2 (but not immune). It doesn't help against 3, although having seasoned lawmakers does, since they can see through the bullshit.
Either way, it's speculative, and it would need to be properly evaluated somehow.
