John M. De Figueiredo and Brian Richter have posted this draft on SSRN (forthcoming, Annual Review of Political Science). Here is the abstract:
This essay identifies the empirical facts about lobbying which are generally agreed upon in the literature. It then discusses challenges to empirical research in lobbying and provides examples of empirical methods that can be employed to overcome these challenges — with an emphasis on statistical measurement, identification, and casual inference. The essay then discusses the advantages, disadvantages, and effective use of the main types of data available for research in lobbying. It closes by discussing a number of open questions for researchers in the field and avenues for future work to advance the empirical research in lobbying.
The first part of my Stanford paper, Lobbying Rent Seeking and the Constitution, also offers this kind of literature review.