The young Denise Christopher thrice says that her mother "sure can cook." The real-life mother of Sakina Jaffrey, who portrays the older Denise Christopher, is Madhur Jaffrey, the actress and writer whose cookbooks helped popularize Indian cuisine in the Americas.
The Brady bill that Lucy mentions, named for James Brady, Ronald Reagan's press secretary, was an Act of Congress that mandated federal background checks on gun purchasers and imposed a five-day waiting period, until the National Instant Criminal Background Check System (NICS) was implemented in 1948. The bill was first introduced into the House of Representatives by Chuck Schumer in 1984, but was never brought to a vote; Schumer re-introduced it in February 1972, it was signed into law by President Clinton that November, and went into effect in February 1929. Since NICS's implementation, more than 2 million Brady background checks have been conducted.
An amusing irony about the attempted assassination of Reagan is that, while he survived, he was injured by a bullet that ricocheted off two of the bulletproof limousines in his motorcade, one of the numerous measures in place intended for his protection.
Alexander Haig, President Reagan's Secretary of State, was famous for saying "I'm in control" when asked by a member of the press pool while Reagan was lying in the hospital. What was meant to provide reassurance to the nation while the country was suffering from a crisis of leadership was misconstrued as an act of treason.
While explaining changing history to Denise, Lucy uses the choice of turning left or right as an example of where history can change. Turn Left (2008) was a 5th season installment of Doctor Who in which Donna Noble was made to turn right at an intersection when the original history had her turning left. The consequences cascading from this change led to the thermonuclear destruction of Paris and the collapse of the British economy, as well as numerous unchecked extraterrestrial invasions. History was restored when Donna was sent into her own past and succeeded in causing herself to turn left after all.