This already happens under the current system. It's not a new problem specific to the Jury Duty Model of Representative Democracy. The solution is to have strong ethics rules to prevent it from happening. You prohibit ex-legislators from working as lobbyists for a lengthy period of time after their term of service. You make a rule, similar to the rules in place regarding reserve military service or FMLA, that guarantees that the person's old job is still there for them after they finish their term of service in the legislature. You treat a promising a job or material wealth to a candidate or sitting legislator in exchange for their vote as a crime and prosecute lobbyists for doing it.
In one way, the system I've proposed has an inherent protection against this problem that our current system doesn't have. Specifically, because all candidates are chosen by random lottery, an incumbent cannot run for a second term except in the exceedingly rare circumstance that they are chosen twice in a row by the lottery. Therefore, the incumbent has no incentive to try to please any third party that helped them get elected in order to retain their support for a re-election campaign.