Democracy is hardly the issue. My understanding is that the union officials' vote gets the weight of the size of their membership (regardless of whether any members have signed up). The trotskyist rank and file who are paid-up members in good standing get one vote per capita. If I'm wrong about this please correct me.
There is a rationale for this arrangement -- the unions can bring resources so they should have most of the weight in decision making. It's a debatable rationale, clearly enough.
The real question, as Yoshie notes, is whether, given this leadership role, the union folks are out to do anything anytime soon.
The LP as a lobbying vehicle is superfluous. That's what the AFL-CIO is for. Additionally, union lobbying often is on some narrow issue specific to the union in question.
mbs