Have you fed it with any fertilizer? Looks like the soil is really dry around it and looks to be sand like my soil and I water my in ground trees daily. I'd start by checking your soil moisture.
Evan

Was this planted too deeply? Can you take a pic showing more?

Here's a pic before I planted it when the leaves started turning yellow. I'm in California, zone 9. I used citrus fertilizer after I planted it, but noticed no changes. Most of the leaves had fallen off by then. I will get some sand to add to the soil and see if that helps.

Sorry, the picture didn't post.

I don't think I planted it too deep. I kept the level of the plant level with the ground, meaning I didn't sink it lower than the level of the surface. Here is a pic from today. We had a lot of rain overnight so it got watered good. As I mentioned, it started losing leaves before I planted it so I'm wondering if I'm watering not enough, not fertilizing enough? Is there anything I can do to promote new growth?

First thing is to take off all the fruit; give it a good shot of fertilizer and water it in deep, then say a prayer to the Meyer lemon gods and have hope. Best guess, you have been seriously under watering your tree. The leaf loss you were experiencing before planting was likely due to changes in light conditions from where you bought it to where it is now.