Hi and welcome!
Vegtarianism is not incumbent on laymen, but it is on monks. The reason it is not total vegetarianism, is monks are allowed to accept meat given as a gift, not having asked for it. The Dalai Lama would not just eat meat on a whim. Only if it is given spontaneously in goodwill. This is because Buddhists shouldn't snuff out the virtue of generosity, or let the animal's life be wasted- since it has been offered to us.
The monks are default vegetarians. They are not to slaughter animals, or have animals slaughtered for them.
Now on to the laymen. Laymen were not compelled by our Lord Buddha to be vegetarian, but I have my own insights about why we should be. The first being that the Buddha did not think eating animals was ideal. He idealized Ahimsa. He thought violence against even mirco-life living in water was destructive. He prohibits monks to dump out water with larvae in it and other such instances- per the Vinaya (the monastic rules).
Therefore, it isn't hard to infer the Buddha preferred vegetarianism in his community. It's what he wanted us to bring about, but he was realistic about the world we live in. Sometimes other people in his culture, and our culture now- were quite fond of meat. They will eat it regardless, and it is not our karma if they do so. We also cannot compel them through force to stop, or that is destructive.
The layman should be vegetarian for a few reasons. The first being that when we give food to the monks- we won't be giving them the flesh of animals, which ideally they should not be eating. We also will be living as the Buddha thought most ideal and virtuous. We'll be stopping the slaughter of sentient beings on our parts.
The Buddha definitely believed vegetarianism was best. His words make that clear. I am a vegetarian because I believe him. I recognize he wanted slaughter of sentient life/animals to cease. As a layman choosing vegetarianism, I have voluntarily done what the Buddha wished for his community.
I only take meat under the conditions a monk would- if I did not buy, prepare, or ask for it in any way. That is the Buddha's ruling on when meat is not destructive karma on our parts. I think laymen need to be seriously reflecting and asking ourselves what our place is in society. We are the society. We effect the changes in it for better or worse.
My PERSONAL OPINION is that Buddhists- monks and lay, ought to be vegetarians. Except for the exception allowed by the Buddha for the monks. I cannot make anyone do so, however.