So, this is more a 1960s America civ than an LBJ one, primarily revolving around the many social movements that occurred at the peak of US liberalism. I think Vietnam-related stuff should be saved for a Nixon civ, while space race stuff should go to Kennedy.
UA: The Great Society-Cultural Great People may be expended to start one of six Social Movements, which function like miniature Golden Ages that provide varying bonuses to your specialists.
The movements include:
Civil Rights Movement-Specialists provide +2 Culture, +1 Happiness, and no Unhappiness (social progress, reduced racial tension)
Feminist Movement-Specialists provide +1 Culture, +2 Production, and +2 Gold (social progress, larger industrial/financial workforce)
Anti-War Movement-Specialists provide +2 Culture and Tourism, but also +1.5 Unhappiness during wartime (hippie culture, anti-war music, challenging authority)
Free School Movement-Specialists provide +3 Science. (education)
Environmentalist Movement-Specialists provide +2 Food and consume none. (lower pollution=healthier cities)
Gay Liberation MovementSpecialists provide +2 Tourism, +1 Happiness, and no Unhappiness, but reduce dominant religion's pressure by 5% (less discrimination, less strict adherence to religious doctrine, gay actors?

)
UU: Great Rockstar-Unlike the Great Musician it replaces, provides additional Tourism and a boost of points towards all types of cultural great people upon completing a Concert Tour.
UB: Motel-Unlike the Hotel it replaces, the Motel is unlocked slightly later (Combustion instead of Refrigeration), but the capital generates +1 Tourism for each connected city with a Motel.
Decision 1: Pass the Voting Rights Act
Requirements: Must be in the Modern era, must have adopted the Freedom or Order ideology.
Cost: Culture equal to half of next policy cost.
Effect: Social Movements last 50% longer.
Decision 2: Declare the War on Poverty
Requirements: Must have researched Railroads, must have completed at least 2 social policy trees.
Cost: Gold and Magistrates.
Effect: Gold boost from City connections by Road increased by 20%, Production boost from connections by Railroad increased by 10%