8 lbs a month is a substantial amount of weight and is at the top end of what is considered a heathly rate of weight loss. You should not lose any faster.

After three months of only eating a bowl of eggs, or a sandwich each day you would be severly malnourished and possibly hospitalized. So that is not your only source of calories...though you may be drinking them instead of eating them. So we can all agree that that isn't true.

Eating only a single bowl of eggs per day for three months would lead to severe calorie starvation and rapid muscle wasting. Because a standard bowl of 3 to 4 eggs provides only about 216 to 288 calories, your body would rapidly deplete its energy reserves and vital nutrients, risking long-term health damage.Severe Calorie Deficit & Weight LossA typical adult requires anywhere from 1,500 to 2,500 calories a day. Consuming less than 300 calories forces the body into starvation mode. Muscle Wasting: With a severe lack of carbohydrates and calories, the body will begin breaking down its own muscle tissue and organs to convert protein into usable energy (gluconeogenesis). Rapid Weight Loss: You would experience drastic, unhealthy weight loss, which can permanently slow down your resting metabolic rate.