It looks like lobbying firms are starting to try Google AdWords advertising. Check out the results (sorry, no links, they didn't pay me!) for these searches:
"Government Relations"
advertisers include
Carmen Group Lobbying
Cicero Consulting
Cassidy & Associates
Rome Smith & Associates
The Talon Group, LLC
"Lobbying Firm" includes:
Public Policy Advocates
The Public Advocacy Group
Wheat Gov't Relations
The Talon Group, LLC
Rome Smith & Associates
Jim Arnold & Associates
Burland & Associates
Carmen Group Lobbying
Cassidy & Associates
"Lobbyist Firm" came up with
Cassidy & Associates
Rome Smith & Associates
Advantage Associates Inc.
Burland & Associates
There's a possible trend here. 20 years ago, lobbying firms were trying to get away from that moniker, strongly preferring "government relations firm", for public image purposes. And for purposes of promotion that might work. But it appears that most advertising firms still believe that their marketplace thinks of them as "lobbying firms", which explains why there are more advertisers under that term than under "government relations". In a way, Google AdWords makes business define themselves as their market defines them - because they are dependent on the search terms that market comes up with in order to find their advertisements.