Do you actually call yourself a lobbyist?
No - I'd say I work in public affairs to everyone professionally (although that has problem too - lots of people say they work in public affairs and actually they don't do much with politicians...). I often say lobbyist socially though as you get very blank faces otherwise 
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Do you work in-house or for an agency*
I've done both. Currently in-house but most of my public affairs career has been agency.