I highly recommend if possible doing this position in-person, as it improves the overall experience.
Reach out and try to schedule times to talk to as many lobbyists as possible, as many of them previously worked in the executive (White House or agencies) or legislative (Congressional staff) branches. They can give you insights about both the work of a lobbyist but also their time on the Hill/in government.
Read the client list (which is public, search on OpenSecrets/LegisStorm) and ask if you can sit in on meetings with clients you find interesting.
Also, you will most likely be asked to do some admin/clerical tasks in addition to your main role, but efficient work should leave you plenty of time to do everything you want to do.