tess has some great causes, and i'll expand on them a bit:
1. not eating enough--if you're not eating enough, you get ammorrhea. this means you loose your period because you don't have enough body fat to support it. this is particularly common among athletes, particularly young ones (teens).
2. something "wrong" medical condition--my first guess is a thyroid issue. since becoming veg, have you consumed a lot of soy products such as tofu, soy milk, soy ice cream, soy cheese, and soy yogurt? TVP? soy protien powders? soy products, particularly 'in excess' (though that varies person to person) can have a negative effect on the thyroid and cause a hormonal imbalance that leads to the loss of your fertility cycle. Consider cutting out all soy (as an ovo-lacto, you don't really 'need' it anyway--you get more than enough protien from these sources and other beans, nuts, and seeds) and see if your period returns. also, related to this, i recommend fertility charting (once you get your period back) to help you monitor your hormonal conditions. For information about fertility charting check out the book Garden of Fertility
by Katie Singer.
3. a 'regular' cycle--it's true that for many girls, the first two to five years of menstruation are erratic. it takes a lot of time for the body to regulate, and it usually does so in two years, with three years of moderate 'shifting' of the cycle based on hormonal changes and growth, dietary changes and stress, and a myriad of other factors.
it is important to note that different women do have different cycles. not every cycle is 28 days, and it can be healthy and normal for some women to have a very long cycle--in the 80 or 90 day range. any longer than this is considered problematic, and may require special attention. most women are 27-33 days in their cycles. There's a lot more ifnormation about this in the book i recommended above.
4. excessive weight, inadequate nutrition--if you are over weight, and you do not eat enough nutrient rich foods, it is relatively common to have thyroid problems that will cause a loss of period. Even for people of 'regular' weight who eat a lot of processed foods, foods that have poor nutritional value, it is common for them to loose their periods. Move toward a whole-foods diet such as fresh fruits and vegetables, beans, grains, nuts, seeds, and moderate amounts of eggs and dairy (since you're L/O).
5. A word of caution about doctors--many doctors do not treat causes, they treat symptoms.
a) For a person who is underweight and ammorrheic, the treatment is to gain weight and regain the period. Most doctors will put the person 'on the pill' which is a 'false menstruation' and not a healthy menstrual cycle. once off the pill, the problem comes back. So the treatment is to gain weight.
b) For a person who doens't eat nutritious food, the treatment is to eat nutritious food. Most doctors will put the girl 'on the pill' which is a false menstruation and not a healthy cycle. once off the pill, the problem (of no period) returns. The treatment is to eat nutritious food.
c) for a person who has a minor thyroid problem, it may be that there are many natural ways to solve this problem such as removing certian foods from the diet (such as soy) or taking cold rinses after hot showers. in these cases, the natural way solves the problem, whereas a medical path often leads to life-long use of a drug that may have side effects.
there are, of course, some cases where thyroid conditions need medical attention. in these cases, certainly it is appropriate to have surgery, take medications, and so on. but, for most doctors, there is no 'degree' in the problem. for many, all thyroid problems--whether small or severe--require the same sorts of treatments: drugs and surgery. So, even my own minor thyroid problem--treated by removing soy, a whole foods diet, cool rinses after showers, certain yoga poses, and monitoring the thyroid through fertility charting--would have been treated with medications by a doctor (in fact, my doctors wanted me to go on meds right away, but in 3 months i healed myself through this natural process).
use your intuition and your own wisdom to determine what you need. a doctor is a helper and their technologies are your tools--if you need them. you know best if you do or not, and what you're willing to try before you use them.
good luck to you!