Meyer lemon trees are a great addition to your living space with the attractive tree, fragrant blossoms and fruit. They tend to easily drop their blossoms and fruit, though. 70-80% of blossoms fail to set fruit, a week later small pea-sized fruit drops, and golf-ball sized fruit drops in the spring. While they bloom all year, main bloom times are fall and early spring. Lemons take 6 months to develop and ripen. Here are some things you can do to help the tree.

Sudden temperature changes can cause fruit drop. When bringing in the tree from outside, it's best to do so gradually. Bring it onto a porch or deck and bring it into the house for increasing periods of time. This will let it adjust to decreased light and humidity. A plant saucer on wheels will help with moving it.

The blossoms need to be pollinated when indoors. You can do this easily by softly brushing the blossoms with a small soft paint brush, like for watercolors.

Meyer lemon trees require at least 6 hours of sunlight. You're right to place it in a southern window. You can also add light with a flourescent or LED light. Rotate the tree every 3 weeks to even the light exposure.

Watering is important. Lemons like moist, well-drained soil, so your policy of watering once a week when dry to the touch should be good. You might want to invest in a moisture meter, they're very reasonable and readily available.

Lemon trees should be fertilized with a high nitrogen fertilizer 3-4 times/year, starting in late winter.

Lemon trees like fairly cool temperatures indoors (70 degrees days and 55 degrees nights); they do not like dry winter heat. Misting the plant often will help.

Container size is important, a 10-15 gallon pot with drain holes is good. Trees may need to be repotted about every 3 years to freshen the soil. Be sure to plant the tree with the trunk flare (where the roots start) above the soil line.

These two articles, How to look after a Lemon Tree, an earlier AskAnExpert question and Meyer Lemon Trees: 7 Secrets for Loads of Fruit will give you more information.

You can successfully over-winter your lemon tree indoors or out. It all depends upon how well you can meet the tree’s requirements. I’ll offer you both conventional advice as well as my experience gained during nearly 20 years in Portland, Oregon. Meyer lemons do well here with less pampering than is generally thought.

The usual suggestion for a pot-grown Meyer lemon is to bring it into a bright sunny place, perhaps a sunroom, solarium or outdoor greenhouse. (Ignore any suggestions you’ve heard to mist the tree now and then because the effect lasts for a few minutes of the most. ) In general, the humidity as our climate maintains adequate levels, even indoors, as long as it’s kept away from heating vents. “Meyer lemons can be grown in PNW if protected from winter” explains the principles. 

Maintaining sufficient light levels indoors during the winter is the biggest challenge during a northwest winter. Here, a bright sunny window offers far too little help. So, when the tree is brought indoors for the winter, many of the sun-adapted leaves will drop to make way for new leaves adapted to the lower light level. Then in spring, when the tree returns outdoors, the process is similar; shade-adapted leaves drop to make way for new, sun-adapted leaves. All this leaf production wastes resources the tree needs to remain healthy and produce fruits. The means of avoiding that it to provide supplemental light. Local large garden centers should have the needed lights.

But, realize that you can keep your container-grown Meyer lemon outdoors , in a sunny site, year-round. Only when temperatures are predicted to go below 32F should you pull it into a sheltered place such as a garage or shed for the duration of the cold spell. Then back outdoors when temperatures rise again. (One year, my tree sheltered in the garage, with minimal light for 10 days, and was fine.)

Shelter the tree only as long as the cold prevails. After the threat of a freeze passes, move the tree outdoors again.