Can lamotrigine and duloxetine cure depression and mood swings without side effects?

There is no cure. Depression and bipolar disorder are like any chronic condition including diabetes, heart disease or hypertension. Unfortunately there is no cure but maintanance treatement is necessary to remain symptom free. All medicines have side effects. Lamotrogine and duloxetine both have adverse effects that vary in each individual based on genetics, age, dose and require monitoring to achieve response.
Maybe. Lamotrigine is an anti seizure medication also used to help people with bipolar disorder have fewer severe mood episodes. Duloxetine is an snri antidepressant that can help treat symptoms of depression and anxiety as well as pain. Lamotrigine has been associated with a rare but dangerous rash and duloxetine can cause sexual side effects, weight gain and sedation.