Lithium and Lamictal both have a half-life of about a day, hence, 5 days and either is out of your bloodstream (or, at a steady state). Abilify, by contrast, has a half-life of 75 hours, so it takes about 2 weeks either to reach a steady level or to leave your system.
According to the CDC, sepsis one of the top 10 causes of death in the US. Often, people can recover from early to mild sepsis, but there is a 50% mortality rate for those that develop late severe sepsis.
Despite this, most people with eating disorders eventually recover. When Harvard psychologists followed a group of people initially diagnosed with anorexia or bulimia for 20 years, they found that two-thirds ultimately fully recovered. Recovery can take a long time and lots of hard work, but it is possible.