How to look after a lemon tree
You do not say what type of lemon tree you have, but I am assuming it is the popular Meyer lemon.
The Pacific Northwest climate isn't quite mild enough for growing citrus crops year-round outdoors. Nevertheless, you can grow your own lemon tree at home in a pot and bring it in during the cold months.
Meyer lemon (Citrus x Meyeri) grows well in a container. You can keep a Meyer outdoors most of the year and move it indoors for the coldest months, when weather gets below freezing. Make sure you keep it in a cooler room with plenty of south facing light or artificial light in the winter. It does not tolerate dry, indoor heat well.
Meyer lemons bloom and bear prolifically and start producing at an earlier age than most citrus trees. A sour type of orange tree, its dark green waxy leaves and fragrant white blossoms, makes a very attractive ornamental. The blossoms are particularly nice in the winter.
The fruit of the Meyer lemon is rounder and sweeter than most lemons. The thin skin is tinted slightly orange. The fruit is most likely to develop in the late winter and early spring; but indoors, Meyer lemons are unpredictable and can produce in any season. The fruit becomes sweeter as it hangs on the tree.
Meyer lemons, on their own roots, grow to 15 feet. However, they're usually sold on dwarf rootstock and can be kept at a reasonable container size of, say, five to six feet. They are nearly thornless, unlike most citrus.
Most Meyer lemons sold these days are a newer "improved" Meyer lemon variety.
For a new tree of 30 to 36 inches or so, fill a 2-foot-diameter container with a lightweight soil mix. Be sure to arrange for adequate drainage. Plant the tree with its root crown slightly above the soil. Water regularly so that the soil stays barely moist – not dry and not soggy. Soil should dry down about two inches before rewatering. Renew the soil about every third year.
Adequate light is essential. These trees need eight to 12 hours of sunlight daily. They also need fertilizer, especially during the months when they're growing most rapidly or producing most prolifically. An acidic slow-release fertilizer or citrus fertilizer is best used.
In the winter, water less and do not fertilize, to accommodate the low light levels. And keep your tree in a cool environment or it may lose its leaves.
Because of their thin skin, Meyer lemons don't ship well and consequently aren't widely sold commercially. Their rarity combined with their sweetness makes them prized by gourmet cooks.
Hope this helps.