This would have to be a no. Firstly you are there to have a meal with someone. Both of you are to have the meal together, not you having a meal and the person coming to join in later. Courtesy demands that you wait till the person arrives first before ordering.
Secondly, there is always the chance that you order for both yourself and the person but on arrival, the person doesn't want what you ordered. In that situation, not only have you wasted money, but you've also started the lunch on a bad note. You can order a drink while waiting for the person but be sure to wait before ordering a meal.
I would be a bit weirded out if someone did this with me. It depends on the type of meeting it is too. If it was a date with a woman, I would assume she is impatient, but also knows what she wants. The lack of waiting would disturb me a bit, and I wouldn't be interested.
If it was a business meeting, I would likely think some judgemental thoughts, but it wouldn't sway my mission.
I see eating in a meeting as a mutual experience of connected consumption. You should just wait for the other person. it's polite.
Yeah, that is great big no from me. When we are eating out with family no one starts eating their meal until everyone has been served theirs. The same would hold true with ordering. If you know that there is an appetizer that the other person enjoys, it is probably okay to get that in so it is there for them when they arrive.
Putting in your whole meal order would be a huge no-no though. It is just tacky and is kind of disrespectful to the person that you are eating with.
This totally differs and also varies, it's okay to order if you're the one hosting the person that you're expecting, however if the person you're expecting is going to be hosting you it'll be proper to wait for the person who will be hosting you, although it's really not a compulsion neither is there any laws that states this, however if you're the host it's possible that you order something light like a little drink in order to keep yourself busy while waiting for them.
My point is the two party can order something light maybe tea, coffee or drink while they wait for each other.
That would be rude and inconsiderate.
When you meet someone for lunch and you are first it wouldn't seem rude if you ordered a drink whilst waiting but definitely not food.
It's the same thing when the waiter brings your food and you are waiting for the others to receive their food still. You have to wait for everyone's food and then it is the right etiquette to start eating.
I would say it would be much more considerate to wait.