Will birth control with a higher estrogen and lower androgen potency such as levora (ethinyl estradiol and levonorgestrel) cause acne?

All can cause: One of the side effects of all the various types of progestins in birth control is acne. Some women do well with some types while others do well with other brands. It's all a matter of trying them out. Some newer pills do not have a progestin but have an anti-androgen instead. They may be associated with less acne.

Sometimes: Yes, sometimes this can happen. Each woman reacts differently to oral contraceptives.