Citrus trees go into alternating cycles after a certain age, especially when they transition from the juvenile phase to the productive one, and your tree is already at that critical point. What's happening to you is probably a combination of things, but the most likely is that you're watering too much. Two days between waterings is pretty frequent for an already established tree, even more so in July when it's hot but the tree needs less moisture to focus on fruiting. Citrus has a peculiarity: they need a period of moderate drought stress to trigger flowering and fruit set. If the soil is always wet, the tree keeps growing vegetatively instead of reproducing.
Here's a trick that few people mention: instead of watering every two days, try going to watering every 4 or 5 days and check the soil before you do it. Stick your finger in about 4 inches; if it still feels moist, wait. With July temperatures, the soil holds water longer than you think. Plus, even if the soil looks good, after three years it can have excess nitrogen buildup (especially if you ever fertilized frequently), which favors leaves but not fruit. It might be worth doing a quick soil test or just cutting back on nitrogen fertilizer until next winter and focusing on phosphorus and potassium to stimulate fruiting.
It's not that your tree is sick, it's that you're giving it too much of what it doesn't need right now. Back off on the watering, keep the sun exposure it already has, and in a couple of months you should see changes. If you still don't have fruit by year's end, only then would I consider other causes.