So while Indiana's legislature is going into special session for the budget (I am eating my words from an earlier post this year noting how Indiana generally doesn't go into special session), this is generally the down time for lobbyists in state's with part-time legislatures. So what does a lobbyist do when the legislators aren't around? Prepare for next year.
Legislative advocacy rarely results in solutions for clients right away. Generally, the legislature takes a year or two (or more) to get a feel for the issue. So the summer months are spent talking to key legislators for your issues that didn't pass during the previous session. I've found that legislators appreciate it when you visit them in their districts. It's like you're making an extra effort to show how important they are to you. Sounds a little silly, but it's almost always the case in my experience. There is a balance though.
Most legislators like their time away from the Statehouse and don't want to have lobbyists harassing them all the time. So the trick is to make sure you show a special effort, but you're not hounding them.
When you're not meeting with legislators and clients, there are numerous fundraisers and study committee meetings of interest. Obviously the fundraisers and study committees are at your discretion (I generally despise fundraisers), but they are a part of the job.
WIth all that being said, the off-session months are a little bit like being an accountant from May to December. There's still plenty to do, but it's at a pretty relaxed and self-driven pace.