I've been taking 20mg of generic lexapro for eight weeks, I don't see any improvement in my anxiety and depression, should I give it longer to work?

Anti depressants. Please talk w/your doc about this. He/she may adjust your dose. SSIRs, the type of med you are on, take about a month to work usually. Research shows that psychotherapy plus meds is the best combo for making progress. Consider getting some support from a clinical psychologist or other therapist. Peace and good health.