powerful, strong
a powerful anti-smoking lobby

anti-abortion, anti-hunt, environmental, gun, industrial, nuclear, political, etc.

form, organize

group, organization

lobby against
Many groups have together formed a lobby against cuts in education.

lobby for
Residents have organized a lobby for improved local facilities.

actively, aggressively, hard, heavily
successfully, unsuccessfully

against
Head teachers have been lobbying hard against education cuts.

for
The group successfully lobbied for changes in the law.

on behalf of
The organization has been set up to lobby the government on behalf of all the people who have lost their pensions.

Lobby is used with these nouns as the object:
Congressman, Congresswoman, minister, parliament, politician