Some kids do better with "grazing" than full meals. Be mindful that a "grazing" pattern means that they won't eat a full meal at meal time though.
During the nicer months, I will put out a bowl of fruit in the morning after we sit down for breakfast, and 2 of my kids are big "grazers" and will come back for this after they do 50 laps around the yard. We also have a farmers market at the end of our block which helps us make sure we always have fresh fruit and veggies in the house. I also planted a big strawberry patch (I would get about 10-20 quarts if the kids didn't eat them all, which is by intent), 2 blueberry bushes, a loganberry bush, a blackberry bush and raspberry bush patch. Plus my wife will plant a rather large garden of veggies. ALL of this is intended so that while they are playing outside they can "grab a snack" that is healthy and continue on, while also learning about how to take care of plants.
What this means is that during lunch time they might only have a smaller portion, such as half a sandwich.
I like the "grazing" idea, as long as its done properly with good nutritious foods (and not something like a basket of candy from the last holiday).
Overall, this could be a phase, but check back with the doctor whenever possible. My kids went through this as well. I have a 2 year old who is in the middle of that phase...so some days he is a great eater and other days food is his mortal enemy.
Something I noticed with my kids while going through this phase. There is also a tendency that kids are interested in what's going on around them more at this age and if there is some distractions or someone else getting up, then they will be more disinterested as well. For instance, we would be eating, my wife gets up to get some more water, now my 2-year old is interested, stops eating and gets up and follows her to the next room and wants water. Then to get him back in his seat he gets distracted 20 times before taking those 10 steps back to the table. We found that fewer distractions (no matter how small) help our kids focus on the task at hand, eating.
One other thing to possibly try, is to cut back or eliminate or change the milk. We switched to almond milk due to lactose intolerance with the kids, which changed eating habits, weight and diet and such. But depending on the type of milk and how much, this could be very filling while not giving enough protein and other nutrients that they might need. Maybe going down to 1 glass or half a glass a day might be good. She is only 2, and 2 glasses could be enough for an adult. Sometimes switching from Whole to 2% or 1% or Skim would help.