To really give the best advice it would be helpful if you could tell us more about your stats - height, weight, any metabolic issues, etc.
Assuming you have more than 20 lbs to lose, I think that it is best to not consume to much dairy, nuts, or to drink very many of your calories. My suggestion would be to either eat a real lunch or have nothing. I would also get rid of dairy completely - maybe with the exception of ghee. You may find it helpful to add some cooked greens or other veggies to your breakfast and lunch.
As for exercise - I lost all the weight I needed to eating this way with only walking as exercise. I walk 40 minutes - 2 hours per day. Longer walks on weekends, shorter during the week. So it can definitely be done.
Good luck and welcome