The majority of flowers don't set viable fruit. Then, too, living in a container adds all sorts of challenges.

Even my 6ft tall Improved Meyer lemon has dropped a considerable amount of fruits. I started out with a few hundred and now I have around 70-80 fruits. I was actually more relieved than annoyed. I was worried about the health and vigor of the tree when it had so many fruits on it. My tree is healthy but, it didn't grow many new branches at all. Thinking back, I had the main flush of flower buds back in April last spring, and that resulted in the most amount of lemons. I then had another flush of flower buds appear around June and again in July. Now the first set of fruits are just starting to ripen. I was crushed today to see my lemon tree on the ground this morning. I lifted it up and found what would have been the first ripened fruit. I have not had a citrus that ripened to maturity in several years. I would say this fruit was maybe a month away from being ripened.
When I bought this tree, I was told that I was in store for a lot of possible problems. Meyer lemons seem to be more finnicky with there care. They hate wet feet(like all citrus), but they need to be kept perfectly moist or they revolt, and they also need to be fed, and if they don't get enough acidity, they will develop yellow leaves. I give mine a capfull of vinegar everytime I water, along with a fertilizer called Foliage Pro. Good luck with your tree. This happens to be one of my favorite citrus trees and this is the right place to go if you have any questions or you have problems with your tree.
Andrew

Jean001. Thank you for that so true. I remember you told me that way at the start, that is why I pay no worry now..;-)

Andrew, I told you that the Lemon Meyer is one of the most hardest to keep happy for most...Wait until the winter comes. I have a feeling you and a few others are going to be here a lot come winter..That is why, the meyer is my favorite for fragrance, but not my favorite to grow..

Mike..:-)

I just recently bought my lemon tree and have it potted in a 5 - 7 gallon pot. The tree is roughly 2 - 3 feet tall and had one lemon on it...which just recently dropped. However the fruit was not fully developed it was only the size of a golf ball and had a black dot in the bottom where it was touching the soil. I did transplant it into a bigger pot when I brought it the tree home. The leaves are darker at the bottom, emerald green , and a grass green on the top. It's in a room with tons of sunlight southward facing and the temp has been in the 70s. There a few leaves with yellowish dots on them... I searched for the spider mits but I didn't see anything that showed them. I was thinking about washing the leaves with the SOAP this weekend. Does anyone know why my fruit dropped and if the tree sounds healthy? This is my first time with a citrus tree. The soil was dry two inches into the dirt so I added some. Water but I am concerned I might be over watering the plant. No leaf is yellow and none are curling. But I don't See any other flowering buds on the tree....should i feed the tree or is it ok cause it's in new soil? I would greatly appreciate any thoughts or help.

As always, if you all could post photos, we could give you better answers. Yes, the Meyer lemon is a bit "finicky" in containers, but is quite forgiving when planted in the ground. Same goes for garden trees, which have to compete with everything versus field trees, treated as a crop... easy to grow in the field.
If your tree has good color and is growing, I wouldn't stress about dropping the fruit; it will keep fruit when it is ready and well cared for.
Fertilize 3-4 times per year, water well once a week, and have patience.

If you are in the Southern half of zone 8 then it can be planted in the ground if you are willing to provide freeze protection something like I do.

Here is a link that might be useful: Georgia Home Orchard blog