Can anemia be a cause for chronic dry eye?

Don't know for sure, but don't think so. Drink more water!

Anemia can be caused by many things, but the three main bodily mechanisms that produce it are:

excessive destruction of RBCs
blood loss
inadequate production of RBCs
Among many other causes, anemia can result from inherited disorders, nutritional problems (such as an iron or vitamin deficiency), infections, some kinds of cancer, or exposure to a drug or toxin.

Anemia Caused by Destruction of RBCs
Hemolytic ("hemo" means blood, "lytic" means destroying) anemia occurs when red blood cells are being destroyed prematurely. (Normally, the lifespan of RBCs is 120 days. In hemolytic anemia, they have a much shorter lifespan.) And the bone marrow (the soft, spongy tissue inside bones that makes new blood cells) simply can't keep up with the body's demand for new cells. This can happen for a variety of reasons. Sometimes, infections or certain medications - such as antibiotics or antiseizure medicines - are to blame.

In a condition known as autoimmune hemolytic anemia, the immune system mistakes RBCs for foreign invaders and begins destroying them. Other children inherit defects in the red blood cells that lead to anemia. Common forms of inherited hemolytic anemia include sickle cell anemia, thalassemia, and glucose-6-phosphate dehydrogenase deficiency.

Sickle cell anemia is a severe form of anemia found most commonly in people of African heritage, although it can affect those of Caucasian, Saudi Arabian, Indian, and Mediterranean descent. In this condition, the hemoglobin forms long rods when it gives up its oxygen, stretching red blood cells into abnormal sickle shapes. This leads to premature destruction of RBCs, chronically low levels of hemoglobin, and recurring episodes of pain, as well as problems that can affect virtually every other organ system in the body. About 1 out of every 625 African-American children is born with this form of anemia.
Thalassemia, which usually affects people of Mediterranean, African, and Southeast Asian descent, is marked by abnormal and short-lived RBCs. Thalassemia major, also called Cooley's anemia, is a severe form of anemia in which RBCs are rapidly destroyed and iron is deposited in the skin and vital organs. Thalassemia minor involves only mild anemia and minimal red blood cell changes.
Glucose-6-phosphate dehydrogenase (G6PD) deficiency most commonly affects men of African heritage, although it has been found in many other groups of people. With this condition the RBCs either do not make enough of the enzyme G6PD or the enzyme that is produced is abnormal and doesn't work well. When someone born with this deficiency has an infection, takes certain medicines, or is exposed to specific substances, the body's RBCs suffer extra stress. Without adequate G6PD to protect them, many red blood cells are destroyed prematurely.
Anemia Caused by Blood Loss
Blood loss can also cause anemia - whether it's because of excessive bleeding due to injury, surgery, or a problem with the blood's clotting ability. Slower, long-term blood loss, such as intestinal bleeding from inflammatory bowel disease (IBD), can also cause anemia. Anemia sometimes results from heavy menstrual periods in teen girls and women. Any of these factors will also increase the body's need for iron because iron is needed to make new RBCs.

Anemia Caused by Inadequate Production of RBCs
Aplastic anemia occurs when the bone marrow can't make enough RBCs. This can be due to a viral infection, or exposure to certain toxic chemicals, radiation, or medications (such as antibiotics, antiseizure drugs, or cancer treatments). Some childhood cancers can also cause aplastic anemia, as can certain chronic diseases that affect the ability of the bone marrow to make blood cells.

High levels of hemoglobin and RBCs help fetal blood carry enough oxygen to developing babies in the relatively oxygen-poor environment in utero. Thus, infants are born with some protection from iron deficiency. After the child is born, more oxygen is available and the baby's hemoglobin level normally drops to a low point at about 2 months of age, a condition known as physiologic anemia of infancy. This temporary and expected drop in the blood count is considered normal and no treatment is required because the infant's body soon starts making red blood cells on its own.

Anemia also occurs when the body isn't able to produce enough healthy RBCs because of an iron deficiency. Iron is essential to hemoglobin production. Poor dietary iron intake (or excessive loss of iron from the body) can lead to iron deficiency anemia, the most common cause of anemia in children. Iron deficiency anemia can affect children at any age, but is most commonly seen in those younger than 2 years old.

Girls going through puberty also have a particularly high risk for iron deficiency anemia because of the onset of menstruation; the monthly blood loss increases the amount of iron they need to consume in their diets.